You wish to test the following claim\( ( H _ { a } ) \)at a significance level of\( \alpha = 0.02 \).

\( H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \)

\( H _ { a } : \mu _ { 1 } \neq \mu _ { 2 } \)

You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size\( n _ { 1 } = 23 \)with a mean of\( M _ { 1 } = 57.7 \)and a standard deviation of\( S D _ { 1 } = 10.2 \)from the first population. You obtain a sample of size\( n _ { 2 } = 23 \)with a mean of\( M _ { 2 } = 59.7 \)and a standard deviation of\( S D _ { 2 } = 6.1 \)from the second population.

What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic =

What is the p-value for this sample? Use conservative degrees of freedom in Stapplet or calculations. (Report answer accurate to four decimal places.)

p-value\( = \square \)

The lifetimes of Brand A tires are distributed with mean 45000 miles and standard deviation 4300 miles, while Brand B tires last for only 36000 miles on the average (mean) with standard deviation 2020 miles. Nicole's Brand A tires lasted 45000

37000 miles and Yvette's Brand B tires lasted 35000 miles. Relatively speaking, within their own brands, which driver got the better wear? Relatively speaking, the driver using the\(\square \)tires got the better wear.

a. Brand A

b. Brand B

While doing an experiment, a physics student recorded the following sequence of elapsed times (in seconds) in a lab notebook.

\( 2.09,24.4,2.91,2.04,2.62,2.26,2.37 \)

When reviewing the calculations later, the student decided that the entry\( 24.4 \)should have been recorded as\( 2.44 \), and made that change in the listing. Find the mean for the new list.

The mean is approximately\( \square \)seconds.

(Simplify your answer. Type an integer or decimal rounded to the nearest hundredth as needed.)

Compute the mean and standard deviation for the sample below, rounding each to the nearest hundredth.

12 , 14 , 17 , 20 , 21 , 24 , 26

The mean of the sample is

(Type an integer or a decimal. Round to two decimal places as needed.)

The standard deviation of the sample is

(Type an integer or a decimal. Round to two decimal places as needed.)

A coin is tossed\( 7 \)times. Find the probability that exactly\( 3 \)are heads. The probability that exactly\( 3 \)are heads is (Type an integer or a simplified fraction.)