Illustrative Exampie \# 4 A sample of 5 measurements, randomi, selected from approximately normally distributed population, with a mean of 4.6 and a standard deviation of 1.5. Test the null hypothesis against the alternative hypothesis \( \mu<6 \). Use \( \alpha=0.05 \).

- بـ أن: \( B=\frac{221}{11} \).

\( \begin{array}{lll}\text { a) } a_{1}=-3 & d=1,5 \quad n=16 \\ \text { б) } a_{1}=121 & d=-3,1 \quad n=25 \\ \text { e) } a_{1}=-2,5 & d=-0,5 \quad n=40 \\ \text { 2) } a_{1}=4,5 & d=0,4 \quad n=100\end{array} \)

Орлуулах аргаар бб а. \( \left\{\begin{array}{c}x^{2}+x y-y^{2}=11 \\ x-2 y=1\end{array}\right. \) а Хоёп тооны ний

1. Given the population \( x_{i}=0,3 \). If a random samples of size 2 are drawn w replacement. a) Find the sampling distribution of the mean \( \bar{x} \). b) Showth \( \mu_{\bar{x}}=\mu, \sigma_{\bar{x}}^{2}=\sigma^{2} / n \)

The lifetime of a 2-volt non-rechargeable battery in constant use has a Normal distribution, with a mean of 516 hours and a standard deviation of 20 hours. The proportion of batteries with lifetimes exceeding 520 hours is approximately 0.5793 0.4207 0.2000