Question

A market research firm has been hired to investigate the variability of retail pricing on an item that is sold in stores in Los Angeles and in San Diego. They gather data from a sample of 21 stores in Los Angeles and 16 stores in San Diego. The sample standard deviations (s) of the sales prices are Los Angeles stores = $12 and San Diego Stores = $14. Determine whether the price variation in these two cities is the same. Use .10 for the level of significance.

Answer 1

The provided sample variances are

s1 = 12 and s_1^2 = 144

s2 = 14 and s_2^2 = 196

and the sample sizes are given by n1​=21 and n2​=16.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

This corresponds to a two-tailed test, for which an F-test for two population variances needs to be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.10, and the rejection region for this two-tailed test is

R={ F : F < 0.454 or F > 2.328}.

(3) Test Statistics

The F-statistic is computed as follows:

(4) Decision about the null hypothesis

Since from the sample information we get that

FL​= 0.454 <  F = 0.735 < FU = 2.328,

it is then concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected.

Therefore, there is not enough evidence to claim that the population variance ​ is different than the population variance ​, at the α=0.10 significance level.

Confidence Interval

The 90% confidence interval for    is:

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