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Hypothesis Testing: test for equal populations variances

A large buyer of household batteries wants to decide which of two equally priced brands to purchase. To do this he takes a random sample of 100 batteries of each brand. The lifetimes measures in hours, of the batteries are recorded in the attached file. Before testing for the difference between the mean lifetimes of these two batteries, he must first determine whether the underlying population variances ar equal.

a. Perform a test for equal population variances. Report a p-value and interpret its meaning.

b. Based on the conclusion in part a, which test statistic should be used in performing a test for the existence of a difference between population means?


Solution Preview

Please see the attached file.

Day Operator 1 Operator 2 Hypotheses: H0: s1^2 = s2^2 vs. HA: s1^2 ≠ s2^2
1 33 31 Level of Significance:a = 5%
2 29 32 Decision Rule: Reject the null hypothesis if p-value < 0.05
3 38 25 Calculations: F = s1^2/s2^2 = 19.26/21.03 = ...

Solution Summary

The solution uses hypothesis testing to test for equal populations variances for household batteries. The p-value and intercept are reported.