Question

Test the hypothesis that the mean price of a book ph is 70 TL (Hop, 70) with the alternate hy pothesis that it is different from 70 TL, at the confidence level of 95 % 4. The price of the book is assumed to be normally distributed with a standard a, of Ifthe mean price estimated for this book based on the prices at N-37 bookstores, is x-67 TL If the mean price estimated for this book based on the prices at N-93 bookstores, is R-67 1L . b.

Answer 1

Null and alternative hypothesis:

$H_o:\mu_x =70$

$H_a:\mu_x\neq 70$

Confidence level = 95%

Significance level, $\alpha$= 100-95= 5%= 0.05

Critical value at $\alpha$ = 0.05 is, $z_{\alpha/2}$ = 1.96

Standard deviation, $\sigma_x$ = 10

a) Sample size, N= 37,

sample mean price, $\bar x$ = 67

Test statistic:

$z = \frac{\bar x - \mu_x}{\sigma_x/\sqrt{n}} = \frac{ 67 - 70}{ 10/\sqrt{ 37}} = \textbf{-1.825}$

As |z| =1.825 < _{$z_{\alpha/2}$} = 1.96, we fail to reject the null hypothesis.

There is not enough evidence to claim that the mean price of a book is different than 70, at the 0.05 significance level.

b) Sample size, N= 93

sample mean price, $\bar x$ = 67

Test statistic:

$z = \frac{\bar x - \mu_x}{\sigma_x/\sqrt{n}} = \frac{ 67 - 70}{ 10/\sqrt{ 93}} = \textbf{-2.893}$

As |z| =2.893 > _{$z_{\alpha/2}$} = 1.96, we reject the null hypothesis.

There is enough evidence to claim that the mean price of a book is different than 70, at the 0.05 significance level.