A pack of trading cards contained \(7\) normal cards and \(2\) special cards. Weihua and John each bought a box of \(40\) packs of card. After opening their cards, they decided to trade with each other for the cards they wanted. \(3\) normal cards were traded for each special card. After trading, Weihua was left with a total of \(384\) cards.
(a) How many cards did John have in the end?
(b) How many special cards did Weihua have in the end?
A scientist begins with \( 20 \) bacteria cells that grow in number at a relative rate of \( 2 / 7 \) per week. Write a function equation to represent \( C ( w ) \) , the number of cells after \( w \) weeks. Then use your equation to determine how long it will take until there are \( 200,000 \) cells. DO NOT use a decimal approximation for the relative rate. Write your equation using fractions and use them in your calculations. Do not round until you have your final answer. Round your final answer to the nearest tenth.
It will take about weeks.
The syllabus for one of your classes has the following information for determining the final weighted grade in the class.
Homework: \(20 \% \quad\) Exams: \(40 \% \quad\) Projects: \(10 \% \quad\) Final Exam: \(30 \% \)
Calculate the course grade as a weighted average if you had a \( 62 \) average on homework, \( 71 \) average on exams, \( 86 \) average on projects and an \( 88 \) on the final exam.
Weighted Course Grade:
Jonny got the following scores in math class: \( 45 \) , \( 60,60,55 \) . He studies hard, and he got \( 100 \) on the final. Please answer the following statistics- increase, decrease, stays the same or can't be determined.
A) MEAN?
B) MEDIAN?
C) MODE?
D) Standard Deviation?
Michaela's quiz scores in Math for this trimester are listed below. What is the minimum score that Michaela needs on her last quiz for her mean quiz grade to be an \( 85 \% \) or above?
\( 72 \% , 77 \% , 84 \% , 86 \% , 92 \% , 94 \% \)
An observational study of teams fishing for the red spiny lobster in a certain body of water was conducted and the results published in a science magazine. One of the variables of interest was the average distance separating traps - called "trap spacing" - deployed by the same team of fishermen. Trap spacing measurements (in meters) for a sample of seven teams of fishermen are shown in the accompanying table. Of interest is the mean trap spacing for the population of red spiny lobster fishermen fishing in this body of water. Complete parts a through \( f \) below.
Click the icon to view the trap spacing data.
a. Identify the target parameter for this study.
The target parameter for this study is
Sean pays \( £ 10 \) for \( 24 \) chocolate bars. He sells all \( 24 \) chocolate bars for \( 50 p \) each. Work out Sean's percentage profit.
The probability of flipping a coin and landing on tails is \( 1 / 2 \) . If you flip the coin \( 100 \) times, approximately how many times could you expect to land on tails?
\( 50 \) times
\( 200 \) times
\( 100 \) times
\( 25 \) times
ldentify hypothesis, Part I; Write the null and alternative hypotheses in words and then symbols for each of the following situations.
A tutoring company would like to understand if most students tend to improve their grades (or not) after they use their senvices. They sample \( 200 \) of the students who used their service in the past year and ask them if their grades have improved or declined from the previous year.
In symbols, the hypotheses are:
A. \(H 0 { : } p = 100 \)
\( { Ha } { : } p > 100\)
B. \(H 0 : p = 0.50 \)
\( H a : p > 0.50\)
C. \(H 0: p = 0.50 \)
\( H a : p \geq 0.51\)
D. \(H 0: p = 100 \)
\( H a : p \geq 101\)
Coupons Driving Visits: A store randomly samples \( 603 \) shoppers over the course of a year and finds that \( 142 \) of them made their visit because of a coupon they'd received in the mail. Construct a \( 95 \% \) confidence interval for the fraction of all shoppers during the year whose visit was because of a coupon they'd received in the mail. (please round all proportions to four decimal places) a) Estimate the true proportion of shoppers during the year whose visit was because of a coupon they'd received in the mail.
( )
Below is a dot plot showing the number of laps each member of the track team ran. Which measure of center would be the best to use to describe the data set?
A. Mean B. Median C. Mode
A store owner wants to know which flavour of juice has the highest number of sales.
Which information would best help the store owner answer this question?
A. total sales of one flavour of juice for one week
B. sales of juice by flavour for one hour
C. sales of juice by flavour for one month
D. total sales of juice for one year
Of \( 137 \) students attending a college orientation session, \( 27 \) are criminal justice majors. If \( 4 \) students at the orientation are selected at random, d determine the probability that each of the \( 4 \) is a criminal justice major. Assume that selection is to done without replacement.
Set up the problem as if it were to be solved, but do not solve.
An irregular figure is framed inside of a \( 10 \) by \( 6 \) foot rectangular. To find its area, \( 2,200 \) random points are generated, and \( 925 \) of them land inside the irregular region. What is the area of the irregular region, to the nearest integer?
\(42 \) sq925uare feet
\( 60 \) square feet \( 42 sq \)
\( 25 \) square feet
\( 35 \) square feet
Quinn is playing a game in which she has a \( 30 \% \) chance of winning \( \$ 5.00 , \) a \( 20 \% \) chance of winning \( \$ 2.00 \) and a \( 50 \% \) chance of winning \( \$ 10.00 . \) Find the expected value.
A. \(\$ 7.50 \)
B. \( \$ 4.50 \)
C. \( \$ 8.00 \)
D. \( \$ 5.00\)
An irregular figure is framed inside of a \( 8 \) by \( 8 \) foot square. To find its area, \( 2,000 \) random points are generated, and \( 850 \) of them land inside the irregular region. What is the area of the irregular region, to the nearest integer?
\(43 \) square feet
\( 64 \) square feet
\( 37 \) square feet
\( 27 \) square feet
A spinner contains \( 8 \) equal sections. Five of the sections win the player \( 10 \) points, \( 2 \) sections win \( 20 \) and one section wins \( 50 \) points. What is the expected value of the spinner?
A. \(16.25 \) points
B. \( 18.75 \) points
C. \( 17.5 \) points
D. \( 15 \) points
About \( 3 \% \) of the population has a particular genetic mutation. \( 400 \) people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of \( 400 \) . (If possible, round to \( 1 \) decimal place.)
About \( 1 \% \) of the population has a particular genetic mutation. \( 200 \) people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of \( 200 \) . (If possible, round to \( 1 \) decimal piace.)
About \( 7 \% \) of the population has a particular genetic mutation. \( 900 \) people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of \( 900 \) . (If possible, round to \( 1 \) decimal place.)
Assume that the probability of a being born with Genetic Condition B is \( p = 2 / 3 . \) A study looks at a random sample of \( 935 \) volunteers.
1. Find the most likely number of the \( 935 \) volunteers to have Genetic Condition B. (Round answer to one decimal place.)
2. Let \( X \) represent the number of volunteers (out of \( 935 \) ) who have Genetic Condition B. Find the standard deviation for the probability distribution of \( X \) . (Round answer to two decimal places.)
3. Use the range rule of thumb to find the minimum usual value \( \mu - 2 \sigma \) and the maximum usual value \( \mu + 2 \sigma \) .
You are playing a card game, and the probability that you will win a game is \( p = 0.23 \) .
If you play the game \( 999 \) times, what is the most likely number of wins?
(Round answer to one decimal place.)
Let \( X \) represent the number of games (out of \( 999 \) ) that you win. Find the standard deviation for the probability distribution of \( X \) . (Round answer to two decimal places.)
The range rule of thumb specifies that the minimum usual value for a random variable is \( \mu - 2 \sigma \) and the maximum usual value is \( \mu + 2 \sigma \) . You already found \( \mu \) and \( \sigma \) for the random variable \( X \) .
Use the range rule of thumb to find the usual range of \( X \) values. Enter answer as an interval using square- brackets and only whole numbers.
You want to obtain a sample to estimate how much parents spend on their kids birthday parties. Based on previous study, you believe the population standard deviation is approximately \( \sigma = 31.9 \) dollars. You would like to be \( 95 \% \) confident that your estimate is within \( 1 \) dollar(s) of average spending on the birthday parties. How many parents do you have to sample?
\( n = 4\)
Syd is registering for classes for the next semester. He can choose from Biology, Chemistry, or Ecology for a science class and from volleyball, bowling, or golf for a physical education class. He can register for only one science class and one physical education class. Which of the following pairs is not a possible combination of classes?
A. Chemistry and golf
B. Biology and golf
C. volleyball and golf
D. None of these
The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is \( 79 \) for a sample of size \( 50 \) . Assume the population standard deviation is \( 5.9 \) . Estimate how much the drug will lower a typical patient's systolic blood pressure (using a
\( 95 \% \) confidence level). Assume the data is from a normally distributed population. Round answers to \( 2 \) decimal places where possible.
< <
The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is \( 79 \) for a sample of size \( 50 \) . Assume the population standard deviation is \( 5.9 \) . Estimate how much the drug will lower a typical patient's systolic blood pressure (using a \( 95 \% \) confidence level). Assume the data is from a normally distributed population. Round answers to \( 2 \) decimal places where possible.
Suppose that textbook weights are normally distributed. You measure \( 22 \) textbooks' weights, and find they have a mean weight of \( 32 \) ounces. Assume the population standard deviation is \( 10.3 \) ounces. Based on this, construct a \( 90 \% \) confidence interval for the true population mean textbook weight. Round answers to \( 2 \) decimal places.
The results of a common standardized test used in psychology research is designed so that the population mean is \( 165 \) and the standard deviation is \( 40 \) . A subject earns a score of \( 245 \) . What is the \( z \) -score for this raw score? Do not round your answer.
z-score \( = \)
The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of \( 60 \) ounces and a standard deviation of \( 11 \) ounces. Use the Standard Deviation Rule, also known as the Empirical Rule (see image below). Do not use normalcdf on your calculator. Suggestion: sketch the distribution in order to answer these questions.
a) \( 99.7 \% \) of the widget weights lie between
b) What percentage of the widget weights lie between \( 38 \) and \( 93 \) ounces?
c) What percentage of the widget weights lie above \( 49 \) ?
9. A recent report indicated that \( 46 \% \) of Canadians spend at least results are considered accurate with a margin of error of \( \pm 3.8 \% \) , Which of the following statements about the confidence is true? A. The confidence level of the report is \( 46 \% \)
B. The confide interval is \( 16.2 \% - 23.8 \% \)
C. The confidence level of the report is \( 90 \% \)
D. The confide interval is \( 42.2 \% - 49.8 \% \)
In a geography class, \( 9 \) students are scheduled to give their presentations today. One student has to leave early for an appointment, so he will present first. How many different ways are there to schedule all of today's presentations?
A. \( 362880 \) C. \( 40320 \)
B. \( 8 \) D. \( 3628800\)
How many permutations are there of the \( 7 \) digits in the number \( 8362754 \) ?
A. \( 720 \) C. \( 5040 \)
B. \( 42 \) D. \( 7\)
A teacher has a list of her \( 20 \) students in alphabetical order. To choose students to participate in a demonstration, she flips a coin. If the coin lands heads, she selects the first \( 10 \) students on the list, and if the coin lands tails, she selects the last \( 10 \) students on the list. Which statement best describes this situation: her method contains sampling bias, her method contains measurement bias, or her method contains no bias?
Suppose we want to choose \( 5 \) letters, without replacement, from \( 9 \) distinct letters.
(a) If the order of the choices does not matter, how many ways can this be done?
(b) If the order of the choices matters, how many ways can this be done?
Based on a sample survey, a company claims that \( 86 \% \) of their customers are satisfied with their products. Out of \( 1,100 \) customers, how many would you predict to be satisfied?
\( 746 \) customers
\( 796 \) customers
\( 946 \) customers
\( 846 \) customers
If you roll a standard number cube \( 95 \) times, how many times do you expect the cube to show a one or a three?
Round your answer to the nearest whole number if needed.
Thirty-seven students in a math course, which was \( 96 \% \) of the students registered in the course, earned a passing grade for the course. Find the number of students registered for the math course. Round your answer to the nearest student if needed.
You wish to test the following claim ( \( H _ { a } \) ) at a significance level of \( \alpha = 0.002 \) .
\( H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \)
\( H _ { a } : \mu _ { 1 } > \mu _ { 2 }\)
You believe both populations are normally distributed, but you do not know the standard deviations for either. And you have no reason to believe the variances of the two populations are equal You obtain a sample of size \( n _ { 1 } = 11 \) with a mean of \( \overline { x } _ { 1 } = 79.4 \) and a standard deviation of \( s _ { 1 } = 14.8 \)
from the first population. You obtain a sample of size \( n _ { 2 } = 11 \) with a mean of \( \overline { x } _ { 2 } = 69.3 \) and a standard deviation of \( s _ { 2 } = 12.9 \) from the second population. a. What is the test statistic for this sample? test statistic \( = \) Round to \( 3 \) decimal places. b. What is the p-value for this sample? For this calculation, use .
\( p \) -value \( = \square \) Use Technology Round to \( 4 \) decimal places. c. The \( p \) -value is...
less than (or equal to) \( \alpha \)
greater than \( \alpha\)
d. This test statistic leads to a decision to...
reject the null
accept the null
fail to reject the null
You wish to test the following claim \( ( H _ { a } ) \) at a significance level of \( \alpha = 0.05 . d \) denotes the mean of the difference between pre-test and post-test scores.
\( H _ { 0 } : \mu _ { d } = 0 \)
\( H _ { a } : \mu _ { d } \neq 0\)
You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-test samples for \( n = 16 \) subjects. The average difference (post - pre) is \( \overline { d } = - 14.1 \) with a standard deviation of the differences of \( s _ { d } = 40.2 \) .
a. What is the test statistic for this sample? test statistic \(= \square\) Round to \(3\) decimal places.
b. What is the p-value for this sample? Round to \(4\) decimal places. p-value \(= \)
You wish to test the claim that the first population mean is less than the se a significance level of \( \alpha = 0.01 \) .
\( H _ { o } : \mu _ { 1 } = \mu _ { 2 } \)
\( H _ { a } : \mu _ { 1 } < \mu _ { 2 } \)
You obtain the following two samples of data.
a. What is the test statistic for this sample? test statistic \( = \square \) Round to \( 3 \) decimal places.
b. What is the p-value for this sample? \(p\) -value \(= \square\) Use Technology Round to \(4\) decimal places.
A magazine stated that based on a study in \( 2007,78 \% \) of Canadians \( 12 \) years of age and older use the Internet regularly, while \( 96 \% \) of Canadians \( 12 - 17 \) years of age use the Internet regularly. Which statement is true based on these statistics?
A larger proportion of Canadians \( 12 - 17 \) years of age use the Internet regularly than Canadians \( 17 \) years of age and older.
A smaller proportion of Canadians \( 12 - 17 \) years of age use the Internet regularly than Canadians \( 17 \) years of age and older,
About \( 18 \% \) of Canadians \( 12 \) years of age and older do not use the Internet regularly.
none of the above
Bonnie surveyed \( 10 \) students at her school about their favourite classes. Of the students surveyed, \( 2 \) said their favourite class was choir. What is the experimental probability that the next student Bonnie talks to will pick choir? Simplify your answer and write it as a fraction or whole number.
\( P \) (choir)
There are \( 42 \) boys and girls participating in an essay-writing competition. Of the competitors, \( 21 \) are in seventh grade, \( 14 \) are in eighth grade, and \( 7 \) are in ninth grade. What is the probability of an eighth grader winning the competition? Which simulation(s) can be used to represent this situation?
A. The probability is \( \frac { 1 } { 3 } \) . Simulate this situation by rolling a \( 6 \) -sided die, with odd numbers representing seventh graders and even numbers representing eighth graders.
B. The probability is \( \frac { 1 } { 6 } \) . Simulate this situation by picking a card from a deck of cards, with hearts representing seventh graders, diamonds representing eighth graders, and spades representing ninth graders.
C. The probability is \( \frac { 1 } { 3 } \) . Simulate this situation by spinning a spinner with six equal sections, with one section representing ninth graders, two sections representing eighth graders, and three sections representing seventh graders.
D. The probability is \( \frac { 1 } { 6 } \) . Simulate this situation by using a number generator with numbers from \( 1 \) to \( 6 \) , with \( 1 \) through \( 3 \) representing seventh graders, \( 4 \) and \( 5 \) representing eighth graders, and \( 6 \) representing ninth graders.
Suppose that \( y = 5 x + 4 \) and it is required that \( y \) be within \( 0.002 \) units of \( 9 \) . For what values of \( x \) will this be true?
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. This will be true only for the finite set of \( x \) -values .
(Simplify your answer. Type your answer(s) as integers or decimals. Use a comma to separate answers as needed.)
B. This will be true for all values of \( x \) in the interval
(Simplify your answer. Use integers or decimals for any numbers in the expression. Type your answer in interval notation.)
C. The no values of \( x \) for which this will be true.
Ryan has the following data:
\(10 \ ,\ x \ ,\ 15 \ ,\ 16\)
If the mode is \( 10 , \) which number could \( x \) be?
Hugo has the following data:
\(13 \ ,\ 4 \ ,\ 16 \ ,\ 17\ ,\ b\)
If the mode is \( 13 , \) which number could \( b \) be?
Christine has the following data:
\( 13 \ ,\ 13 \ ,\ 11\ ,\ g \ ,\ 15 \ ,\ 2 \ ,13\ ,\ 12\)
If the range is \( 13 , \) which number could \( g \) be?
Diana has the following data:
\(16 \ ,\ 15 \ ,\ 17 \ ,\ 8 \ ,\ 8 \ ,\ 13 \ ,\ 8 \ ,\ 17 \ ,\ 17 \ ,\ b \ ,\ 5\)
If the mode is \( 17 , \) which number could \( b \) be?
Rosa has the following data:
\(18 \ ,\ 19 \ ,\ 15 \ ,\ s \ ,\ 18\ ,\ 13 \ ,\ 15 \ ,\ 14 \ ,\ 18 \ ,\ 15 \ ,\ 16\)
If the median is \( 16 , \) which number could \( s \) be?
A car dealership sells \( 48 \) cars of the same model in one month. The average price of each car is \( \$ 25,000 \) with a maximum variance of \( \$ 3,000 \) due to additional options. What is the range of the total revenue that the car dealership makes for the month's sales of this car model?
A. \( \$ 22,000 \leq x \leq \$ 28,000 \)
B. \( \$ 88,000 \leq x \leq \$ 112,000 \)
C. \( \$ 264,000 \leq x \leq \$ 336,000\)
D. \( \$ 1,056,000 \leq x \leq \$ 1,344,000\)
Decide which method (theoretical, relative frequency, or subjective) is appropriate, and compute or estimate the following probability. A card is drawn at random out of a well-shuffled deck of \( 52 \) cards. Find the probability of drawing a two or three.
Which method is appropriate?
A The theoretical method
B. The relative frequency method
C. The subjective method
The probability of drawing a two or three is
(Type an integer or a simplified fraction.)
You are required to take five courses, one each in humanities, sociology, science, math, and music. You have a choice of \( 5 \) humanities courses, \( 7 \) sociology courses, \( 5 \) science courses, \( 4 \) math courses, and \( 4 \) music courses. How many different sets of five courses are possible?
There are \( \square \) different sets of five courses possible.
(Type a whole number.)
In \( 2015 \) , the highest and lowest death rates in a country were in Regions A and B, respectively. Region A reported \( 22,231 \) deaths with a population of about \( 1.7 \) million. Region B reported \( 10,780 \) deaths with a population of \( 1.8 \) million.
a. Compute the death rates in Region A and B in deaths per \( 100,000 \) people.
b. How many people die each day in Region A?
c. How many people die each day in Region \( B \) ?
a. The death rate in Region A was \( \square \) deaths per \( 100,000 \) people. (Round to the nearest whole number as needed.)
The death rate in Region B was \( \square \) deaths per \( 100,000 \) people. (Round to the nearest whole number as needed.)
b. Each day \( \square \) people die in Region A. (Round to the nearest whole number as needed.)
c. Each day \( \square \) people die in Region B. (Round to the nearest whole number as needed.)
A group of people were asked if they had run a red light in the last year. \( 119 \) responded "yes", and \( 187 \) responded "no". Find the probability that if a person is chosen at random, they responded "yes".
Answer:
A die is rolled. Find the probability of the given event. Write your answers as whole numbers or reduced fractions.
(a) The number showing is a \( 3 \)
\(P ( 3 ) = \)
(b) The number showing is an even number
\(P (\) even \() = \)
(c) The number showing is greater than \(4\)
\( P ( \) greater than 4) \( = \)
The probability that event \( A \) will occur is \( P ( A ) = 0.32 . \)
What is the probability (in decimal form) that event \( A \) will not occur? \( P ( \overline { A } ) = \square \)
What a are the odds for event \( A \) to ?
What are the odds against event \( A \) to ?
Simplify your answers.
Exam results for \( 100 \) students are given below. For the given exam grades, briefly describe the shape and variation of the distribution.
median \( = 69 , \) mean \( = 70 \) , low score \( = 61 \) , high score \( = 96\)
Answer the following True or False:
A researcher wants to test the hypothesis that college students weigh less on average than the average American ( \( 160 \) lbs). The sample mean of the \( 80 \) students who were weighed was found to be \( 142 \) pounds and the p-value was \( 0.03 \) . This means that if the mean of all students' weight is \( 160 \) lbs, then there would be only a \( 3 \% \) chance that a randomly selected group of \( 80 \) students would have a mean weight of less than
\( 142 \) lbs.
True
False
The following list contains the average annual total returns (in percentage points) for \( 8 \) mutual funds. The mutual funds appear in an online brokerage firm's "all-star" list.
\(2,32 , - 7,2 , - 7 , - 7,13,2\)
(a) What is the median of this data set? If your answer is not an integer, round your answer to one decimal place.
(b) What is the mean of this data set? If your answer is not an integer, round your answer to one decimal place.
(c) How many modes does the data set have, and what are their values? Indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the mode(s), if applicable.
\(\begin{array}{|c|c|} \hline \text { Ages } & \text { Number of students } \\ \hline 15- 18 &{2} \\ \hline 19- 22 & 7 \\ \hline 23- 26 & 8 \\ \hline 27- 30 & 4 \\ \hline 31- 34 & \\ \hline 35- 38 & 9 \\ \hline \end{array}\)
Based on the frequency distribution above, find the relative frequency for the class with a lower class limit of \( 19\)
When Brooklyn runs the \( 400 \) meter dash, her finishing times are normally distributed with a mean of \( 76 \) seconds and a standard deviation of \( 3 \) seconds. Using the empirical rule, what percentage of races will her finishing time be between \( 70 \) and
\( 82 \) seconds?
In a mid-size company, the distribution of the number of phone calls answered each day by each of the \( 12 \) receptionists is bell-shaped and has a mean of \( 55 \) and a standard deviation of \( 4 \) . Using the empirical rule (as presented in the book), what is the approximate percentage of daily phone calls numbering between \( 47 \) and \( 63 ? \)
Political pollsters may be interested in the proportion of people that will vote for a particular cause. Match the vocabulary word with its corresponding example.
1. The \( 750 \) voters who participated in the survey
2. Cause: Yes or No to the survey question
3. The list of \( 750 \) Yes or No answers to the survey question
4. The proportion of the \( 750 \) survey participants who will vote for the cause
5. The proportion of all voters from the district who will vote for the cause
6. All the voters in the district
a. Variable
b. Population
c. Parameter
d. Sample
e. Data
f. Statistic
On a recent quiz, the class mean was \(71\) with a standard deviation of \(3.8\) . Calculate the z-score (to \(2\) decimal places) for a person who received score of \(58\) . z-score:
Is this unusual?
Unusual
NotUnusual
"Trydint" bubble-gum company claims that \( 7 \) out of \( 10 \) people prefer their gum to "Eklypse" and they want to test if this value is different.
The null and alternative hypotheses in symbols would be:
A. \(H _ { 0 } : p = 0 . 7\)
\( H _ { 1 } : p > 0.7\)
B. \(H _ { 0 } : \mu = 0.7 \)
\( H _ { 1 } : \mu < 0.7\)
C. \(H _ { 0 } : p = 0.7 \)
\( H _ { 1 } : p < 0.7\)
D. \(H _ { 10} : \mu = 0.7 \)
\( H _ { 1 } : \mu \neq 0.7\)
E. \(H _ { 0 } : p = 0.7 \)
\( H _ { 1 } : p \neq 0.7\)
F. \(H _ { 0 } : \mu = 0.7 \)
\( H _ { 1 } : \mu > 0.7\)
The null hypothesis in words would be:
A. The proportion of all people that prefer Trydint gum is less than \( 0.7 \) .
B. The proportion of all people that prefer Trydint gum is greater than \( 0.7 .\)
C. The proportion of people in a sample that prefer Trydint gum is not \( 0.7\)
D. The average of people that prefer Trydint gum is not \( 0.7 .\)
E. The proportion of people in a sample that prefers Trydint gum is \( 0.7 .\)
F. The proportion of all people that prefer Trydint gum is \( 0.7\)
H. The average of people that prefer Irydint gum is \( 0.7 \) .
Based on a sample of \( 380 \) people, \( 245 \) said they prefier "Trydint" gum to "Eklypse".
The point estimate is: _____
The \( 95 \% \) confidence interval is: ______ to ______
Based on this we:
A. Reject the null hypothesis
B. Fail to reject the null hypothesis
Out of \( 300 \) people sampled, \( 93 \) had kids. Assuming the conditions are met, construct a \( 90 \% \) confidence interval for the true population proportion of people with kids,
Give your answers as decimals, to three places
( )
Based on \( 2017 \) data from DataUSA.
The population of Cincinnati is \( 301,305 \) people. If \( 28.7 \% \) of people in Cincinnati live in poverty, how many people live in poverty?
people in Cincinnati live in poverty
Use the frequency distribution shown below to construct an expanded frequency distribution. High Temperatures \( ( { } ^ { \circ } F )\)
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline \text { Class } & 16- 26 & 27- 37 & 38- 48 & 49- 59 & 60- 70 & 71- 81 & 82- 92 \\ \hline \text { Frequency, f } & 17 & 43 & 66 & 67 & 84 & 66 & 22 \\ \hline \end{array}\)
Complete the table below.
High Temperatures \( ( { } ^ { \circ } F ) \) (Round to the nearest hundredth as needed.)
\(\begin{array}{|l|c|c|c|l|} \hline \text { Class } & \text { Frequency, f } & \text { Midpoint } & \begin{array}{l} \text { Relative } \\ \text { frequency } \end{array} & \begin{array}{l} \text { Cumulative } \\ \text { frequency } \end{array} \\ \hline 16- 26 & 17 & & & \\ \hline \end{array}\)
Construct a frequency distribution and a frequency histogram for the data set using the indicated number of classes. Describe any patterns.
Number of classes: \( 8 \) Data set: Reaction times (in milliseconds) of \( 30 \) adult females to an auditory stimulus .
\(\begin{array}{cccccc} 428 & 291 & 382 & 338 & 514 & 423 \\ 385 & 427 & 374 & 313 & 444 & 390 \\ 350 & 471 & 385 & 413 & 440 & 426 \\ 300 & 455 & 309 & 309 & 323 & 412 \\ 450 & 385 & 322 & 357 & 510 & 415 \end{array}\)
Construct a frequency distribution of the data. Use the minimum data entry as the lower limit of the first class.
This data is from a sample. Calculate the mean, standard deviation, and variance. Please show the following answers to \( 2 \) decimal places.
Sample Mean \(= \square\)
Sample Standard Deviation =
Sample Variance \(= \)
Ooops - now you discover that the data was actually from a population! So now you must give the populaition standard deviation.
Population Standard Deviation =
The following refers to the following data set:
\(\begin{array}{|l|l|l|l|l|l|l|l|l|l|} \hline 37 & 93 & 52 & 64 & 22 & 84 & 20 & 93 & 58 & 35 \\ \hline \end{array}\)
What is the mean \( ( \overline { x } ) \) of this data set?
What is the median of this data set?
What is the mode of this data set?
Which statistic (mean, median, or mode) is most appropriate in each of the following situations?
a. Tables in the dining hall are numbered \( 1 \) through \( 12 \) for students who eat there. The principal calls out a number for the table that will go through the buffet line first. The other tables follow in.order of the table numbers. One student is sure the principal calls certain tables more often. She keeps track of which numbers are called over a \( 21 \) -day period.
A. Mean
B. Median
C. Mode
b. The offensive line of a football team is larger than in previous years. The program will list a statistic to show this fact.
A. Mean
B. Median
C. Mode
c. A reporter is doing a story on the falling prices of homes in a large neighborhood. The reporter wants to demonstrate how the prices have fallen for the typical home, not just the most expensive houses.
A. Mean
B. Median
C. Mode
In a psychology class, \( 28 \) students have a mean score of \( 83.3 \) on a test. Then \( 12 \) more students take the test and their mean score is \( 74.3 \) .
What is the mean score of all of these students together? Round to one decimal place.
Use the frequency distribution shown below to construct an expanded frequency distribution. High Temperatures \( ( { } ^ { \circ } F )\)
\(\begin{array}{|c|c|c|c|c|c|c|c|} \hline \text { Class } & 16- 26 & 27- 37 & 38- 48 & 49- 59 & 60- 70 & 71- 81 & 82- 92 \\ \hline \text { Frequency, f } & 18 & 44 & 68 & 69 & 77 & 68 & 21 \\ \hline \end{array}\)
Complete the table below. High Temperatures \( ( { } ^ { \circ } F ) \) (Round to the nearest hundredth as needed.)
\(\begin{array}{|l|c|c|c|c|} \hline \text { Class } & \text { Frequency, f } & \text { Midpoint } & \begin{array}{l} \text { Relative } \\ \text { frequency } \end{array} & \begin{array}{l} \text { Cumulative } \\ \text { frequency } \end{array} \\ \hline 16- 26 . & 18 & \square & \square & \square \\ \hline \end{array}\)
It is extremely important for a researcher to clearly define the variables in a study because this helps to determine the type of analysis that can be performed on the data. For example, if a researcher wanted to describe people based on Social Security number, what level of measurement would the variable .
"Social Security number" be? Now suppose the researcher felt that certain people who lived farther east received higher numbers. Does the level of measurement of the variable change? If so, how?
What is the level of measurement of the variable "Social Security number" in the original scenario?
A. Ratio
B. Ordinal
C. Interval
D. Nominal
In a recent Super Bowl, a TV network predicted that \( 36 \% \) of the audience would express an interest in seeing one of its forthcoming television shows. The network ran commercials for these shows during the Super Bowl. The day after the Super Bowl, and Advertising Group sampled \( 128 \) people who saw the commercials and found that \( 50 \) of them said they would watch one of the television shows.
Suppose you are have the following null and alternative hypotheses for a test you are running:
\( H _ { 0 } : p = 0.36 \)
\( H _ { a } : p \neq 0.36 \)
Calculate the test statistic, rounded to \( 3 \) decimal places
Which description is represented by a discrete graph?
A. Kiley bought a platter for \( \$ 19 \) and several matching bowls that were \( \$ 8 \) each. What is the total cost before tax?
B. The temperature at \( 9 \) a \( m \) . was \( 83 ^ { \circ } F \) and is heating up at an average rate of \( 6 ^ { \circ } F \) per hour. What is the temperature \( x \) hours later?
C. Juan ate an egg with \( 78 \) calories and some cereal with \( 110 \) calories per serving for breakfast. What is the total amount of calories he consumed?
D. A bottle contained \( 2,000 mL \) of liquid and is being poured out at an average rate of \( 300 mL \) per second. How much liquid is left in the bottle after \( x \) seconds?
Saver Bank's account balances in New Jersey have a normal distribution with mean \( \$ 1,543 \) and standard deviation \( \$ 329 \) . Saver Bank charges a small fee to all customers who are in the bottom \( 4 \% \) . What is the amount of money you should have at the Saver Bank in order to be charged with a small fee.
A. \( 1460 \)
B. \( 967 \)
C. \( 968 \)
D. \( 1543\)
The age in Australia has a normal distribution with a mean \( 45 \) years and standard deviation \( 11 \) years. The children are classified as the youngest \( 33 \% \) of population. At what age do children become adults in Australia.
A. \( 20 \)
B. \( 30 \)
C. \( 40 \)
D. \( 50\)
At a walk-in interview, \( 12 \% \) of candidates can be selected, and \( 28 \% \) of candidates can be put on hold for the next hiring date. If \( 75 \) candidates are interviewed, about how many are expected to be rejected?
A. \( 30 \) B. \( 45 \)
C. \( 9 \) D. \( 21\)
When testing for current in a cable with eight color-coded wires, the author used a meter to test four wires at a time. How many different tests are required for every possible pairing of four wires?
A doctor measured serum HDL levels in her patients, and found that they were normally distributed with a mean of \( 68.7 \) and a standard deviation of \( 3.8 \) . Find the serum HDL levels that correspond to the following z-scores. Round your answers to the nearest tenth, if necessary.
(a) \( z = - 1.15 \)
(b) \( z = 1.54 \)
A certain brand of automobile tire has a mean life span of \( 36,000 \) miles and a standard deviation of \( 2,150 \) miles. (Assume the life spans of the tires have a bell-shaped distribution.)
The life spans of three randomly selected tires are \( 35,000 \) miles, \( 38,000 \) miles, and \( 31,000 \) miles. Find the \( z \) -score that corresponds to each life span.
(a). For the life span of \( 35,000 \) miles, \( z \) -score is _______. (Round to the nearest hundredth as needed.)
(b). For the life span of \( 38,000 \) miles, \( z \) -score is_______. (Round to the nearest hundredth as needed.)
(c). For the life span of \( 31,000 \) miles, \( z \) -score is _______. (Round to the nearest hundredth as needed.)
(d). According to the \( z \) -scores, would the life spans of any of these tires be considered unusual?
A. No
B. Yes
Identify the population, the sample, and any population parameters or sample statistics in the given scenario.
\( 67 \% \) of all instructors at a local university teach \( 2 \) or more classes.
A. Population: instructors at a local university; Sample: none given;
B. Population Parameter: \( 67 \% \)
C. Population: instructors of \( 2 \) or more classes; Sample: instructors at a local university;
D. Population Parameter: \( 67 \% \)
A college's football team will play \( 16 \) games next fall. Each game can result in one of \( 2 \) outcomes: a win or a loss. Find the total possible number of outcomes for the season record.
The Hoffmans are planning their next family night. They always have dinner out somewhere and then do something fun together. There are \( 2 \) adults and \( 5 \) children in the family. Each family member is allowed \( 3 \) meal suggestions and each child is allowed \( 3 \) activity suggestions. Assuming no family members choose the same thing, how many different family night possibilities are there?
The test scores of the students in four classes are summarized below. Answer the questions about them.
Class \( A \) : The range of scores is \( 32 \) and the mean score is \( 129 \) .
Class \( B \) : The range of scores is \( 40 \) and the mean score is \( 127 \) .
Class \( C \) : The range of scores is \( 37 \) and the mean score is \( 122 \) .
Class \( D \) : The range of scores is \( 38 \) and the mean score is \( 120 \) .
(a) Based on the information above, which class's scores have the most variability?
A. Class A B. Class
C. Class C D. D. lass D
(b) Based on the information above, which class has the lowest scores on average?
A. Class A B. Class
C. Class C D. D. lass D
You work for a large farm with many fields of corn. You are investigating the mass of a sample of ears of corn. You gather the following data:
Mass(g) of ears of corn
\(\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|} \hline 12.4 & 12.6 & 13.8 & 15.1 & 15.7 & 15.7 & 16.3 & 17.2 & 17.6 & 17.7 & 18.4 \\ \hline 18.5 & 18.8 & 18.8 & 20.3 & 20.4 & 20.6 & 20.7 & 21.0 & 22.3 & 27.2 & 32.6 \\ \hline \end{array}\)
Some of the masses in the sample seem much larger than the rest. You decide to make several calculations describing the "spread" of the data set. You hope to use them to help in the search for outliers.
Here are your summary Statistics:
\(\begin{array}{|r|r|c|c|c|c|c|} \hline \text { Mean } & \text { St. Dev. } & \text { Min } & \text { Q1 } & \text { Med } & \text { Q3 } & \text { Max } \\ \hline 18.8 & 4.57 & 12.4 & 15.85 & 18.45 & 20.55 & 32.6 \\ \hline \end{array}\)
Find the following:
Apply the \( 1.5 \) IQR rule to search for outliers. Report the lower and upper cutoffs.
a. \( I Q R = \) __________
b. Lower \( = \) __________
c. Upper \( = \) __________
d. Are there any outliers by the \( 1.5 \) IQR rule?
1. Which measure of center is sensitive to extreme values?
A. mean
B. median
C. mode
D. midrange
2. Which measure of center is resistant to extreme values?
A. mean
B. median
C. mode
D. midrange
3. Which measure of dispersion is sensitive to extreme values?
A. IQR
B. Standard Deviation
4. Which measure of dispersion is resistant to extreme values?
A. IQR
B. Standard Deviation
The highway mileage (mpg) for a sample of \( 8 \) different models of a car company can be found below. Find the mean, median, mode, and standard deviation. Round to one decimal place as needed. Use technology.
\( 19,23,25,27,29,31,34,34 \)
It is commonly believed that the mean body temperature of a healthy adult is \(98.6 ^ { \circ } F\) . You are not entirely convinced. You believe that it is not \(98.6 ^ { \circ } F\) . You collected data using \(49\) healthy people and found that they had a mean body temperature of \(98.26 ^ { \circ } F\) with a standard deviation of
\(1.04 ^ { \circ } F\) . Use a \(0.05\) significance level to test the claim that the mean body temperature of a healthy adult is not \(98.6 ^ { \circ } F\) .
a) Identify the null and alternative hypotheses?
\(H _ { 0 } : \) _________
\(H _ { 1 } : \) _________
b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)?
A. left-tailed
B. right-tailed
C. two-tailed
c) Identify the appropriate significance level as a decimal.
d) Calculate your test statistic. Write the result below, and be sure to round your final answer to two decimal places.
e) Calculate your p-value. Write the result below, and be sure to round your final answer to four decimal places.
The blue catfish (Ictalurus Furcatus) is the largest species of North American catfish. The current world record stands at \(143\) pounds, which was caught in the John H. Kerr Reservoir (Bugg's Island Lake) located in Virginia. According to American Expedition, the average weight of a blue catfish is between \(20\) to \(40\) pounds. Given that the largest blue catfish ever caught was at the John H. Kerr Reservoir, you believe that the mean weight of the fish in this reservoir is greater than \(40\) pounds. Use the data below, which represents the summary statistics for \(40\) blue catfish caught at this reservoir, and a \(0.05\) significance level to test the claim that the mean weight of the fish in the John H. Kerr Reservoir is greater than \(40\) pounds.
\(n = 40 ; \quad \overline { x } = 40.94\) pounds; \(s = 4.81\) pounds
a) Identify the null and alternative hypotheses?
\(H _ { 0 } : \) __________
\(H _ { 1 } : \) __________
b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)?
A. left-tailed
B. right-tailed
C. two-tailed
c) Identify the appropriate significance level as a decimal.
d) Calculate your test statistic. Write the result below, and be sure to round your final answer to two decimal places.
e) Calculate your p-value. Write the result below, and be sure to round your final answer to four decimal places.
Super Sandwiches offers \( 4 \) kinds of breads, \( 3 \) kinds of meats, \( 5 \) cheeses, and \( 7 \) dressings for a sandwich. How many possible combinations would there be for making a sandwich?
A. \( 3 \)
B. \( 420 \)
C. \( 7 \)
D. \( 15 \)
E. \( 19\)
Tyler decides which type of pizza to order. The choices for crust are thin crust or regular crust. The choices for one topping are pepperoni, mushrooms, olives, sausage, or green peppers. Tyler has trouble deciding because there are so many possibilities. He selects the type of crust and one topping at random. How many outcomes are in the sample space?
A Scrabble player has four tiles with the letters \( A , N , P \) , and \( S \) .
a. How many arrangements of these letters are possible?
b. Draw a tree diagram that shows how to get the arrangements and explain how a decision chart represents the tree.
c. What is the probability of a two-year-old randomly making a word using the four letters?
Find the mean of the data.
\( 9,12,11,11,10,7,4,8\)
BIG IDEAS MATH Find the mean of the data.
\( 53,45,43,55,28,21,61,29,24,40,27,42 \)
Given the plot of normal distributions \( A \) and \( B \) below, which of the following statements is true? Select all correct answers.
Select all that apply:
(A). \(A \) has the larger mean.
(B). \( B \) has the larger mean.
(C). The means of \( A \) and \( B \) are equal.
(D). \( A \) has the larger standard deviation.
(E). \( B \) has the larger standard deviation.
(F). The standard deviations of \( A \) and \( B \) are equal. ()
What is the range of the following data set?
\( 5,6,7,3,4,5,6,8,7 \)
A. \( 12 \) B. \( 5 \)
C. \( 3 \) D. \( 0\)
