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

Option A , should not be rejected

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\\eq \sigma_1^2`

Generally the equation for test Statistics is mathematically given by

`T=(\sigma_1^2)/(\sigma_2^2)`

`T=(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<T<T_(x')`

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

Option A , should not be rejected