Test the claim about the differences between two population variances ? and ? at

Question

Test the claim about the differences between two population variances ? and ? at the given level of significance ? using the given sample statistics. Assume that the sample statistics are from independent samples that are randomly selected and each population has a normal distribution Claim: ?' > ? , ?-0.05 Sample statistics: s1 635, n18, s2 238, n2-12 Find the null and alternative hypotheses. Find the critical value (Round to two decimal places as needed.) Find the test statistic. (Round to two decimal places as needed.) Choose the correct conclusion below O A. Fail to reject the null hypothesis. There is not enough evidence to reject the claim O B. Reject the null hypothesis. There is enough evidence to reject the claim. ° C. Fail to reject the null hypothesis. There is not enough evidence to support the claim. O D. Reject the null hypothesis. There is enough evidence to support the claim

Explanation / Answer

The statistical software output for this problem is:

Two sample variance summary hypothesis test:
?12 : Variance of population 1
?22 : Variance of population 2
?12/?22 : Ratio of two variances
H0 : ?12/?22 = 1
HA : ?12/?22 > 1

Hypothesis test results:

Hence,

Hypotheses: Option D is correct.

Critical value = 3.01

Test statistic = 2.67

Conclusion: Option D is correct.

Ratio Num. DF Den. DF Sample Ratio F-Stat P-value ?12/?22 7 11 2.6680672 2.6680672 0.0707

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