We are interested in determining whether or not the variances of the sales at two small grocery stores are equal. A sample of 21 days of sales at Store A and a sample of 16 days of sales at Store B indicated the following. Store A Store B n1 = 21 n2 = 16 = 800 = 400 a. Provide the hypotheses to be tested. b. Compute the test statistic. c. Determine the critical value of F at 95% confidence. d. Compute the p-value and use it to test the above hypotheses.

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Netta00 Netta00 · Answer 1 · 2021-06-17T15:54:01+02:00

Answer:

a) Null Hypothesis : H0 : σ1^2 = σ2^2

Alternative Hypothesis: H1 = σ1^2 not equal to σ2^2

b) The test statistics =4

c) 0.03, 2.76

Explanation:

a) Null Hypothesis : H0 : σ1^2 = σ2^2

Alternative Hypothesis: H1 = σ1^2 not equal to σ2^2

b) The test statistics

F=s1^2/s2^2

=800^2/400^2

=4

c) The critical value of F at 95% confidence.

Given a=0.05

The critical value is F(0.025,df1=n1-1=20, df2=n2-1=15)=0.03 from the F tables

F(0.975,df1=20,df2=15)=2.76 from the F tables

topeadeniran2 topeadeniran2 · Answer 2 · 2021-12-28T16:47:05+01:00

Based on the information given, the null Hypothesis will be H0 : σ1² = σ2² and the alternative hypothesis will be H1 = σ1² not equal to σ2².

The test statistics from the information given will be:

F = s1²/s2²

F = 800² /400²

= 4

The critical value of F at 95% confidence will be a = 0.05. Therefore, the critical value is F(0.025,df1=n1-1=20, df2=n2-1=15) = 0.03

Lastly, F(0.975,df1=20,df2=15) = 2.76 from the F tables.

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