Question

Exhibit 11-2 We are interested in determining whether the variances of the sales at two music stores (A and B) are equal. A sample of 25 days of sales at store A has a sample standard deviation of 30, while a sample of 16 days of sales from store B has a sample standard deviation of 20. At 95% confidence, the null hypothesis _____. a. should not be rejected b. should be revised c. should be rejected d. None of these answers are correct.

Answer 1

Answer:

Option A , should not be rejected

Step-by-step explanation:

From the question we are told that:

Sample 1 $n=25$

Standard deviation 1 $\sigma_1=30$

Sample 2 $n=16$

Standard deviation 2 $\sigma_2=20$

Level of  confidence $\alpha=95\%=>0.95$

Generally The Hypothesis are given as

 $H_0:\sigma_1^2=\sigma_1^2$

 $H_1:\sigma_1^2\neq \sigma_1^2$

Generally the equation for test Statistics is mathematically given by

 $T=\frac{\sigma_1^2}{\sigma_2^2}$

 $T=\frac{30^2}{20^2}$

 $T=2.25$

Therefore

Critical Value

 $X=(\alpha,df_1)$

 $X'=(\alpha,df_2)$

Where

 $df=n-1$

Therefore

 $X=(0.95,24)$

 $X'=(0.95,15)$

From Table

 $T_{Critical}=T_x,T_{x'}$

 $T_{Critical}=0.41,2.701$

Therefore

 $T_x$

Hence,We fail to reject the Null Hypothesis $H_0$

Option A , should not be rejected