Two cosmetics manufacturers produce similar hairspray products.Manufacturer 1 asserts that its hairspray holds longer, on average, than does its competitor's product.To test the claim, we randomly sample 20 hairspray users and have half of them use brand 1 hairspray while the other half use brand 2.The average hold time for brand 1 is 18.5 hr with a standard deviation of 6.28 hr.The average hold time for brand 2 is 17.95 hr with a standard deviation of 8.55 hr.Does the sample support manufacturer 1's assertion? Assume that the populations in question are both normal and have unequal variances.Select the appropriate critical value (CV), test statistic (TS), decision and conclusion.(Use α = 0.10).

Question

Quizplus · Accepted Answer

We need to use a two-sample t-test with unequal variances since the population variances are not assumed to be equal. The calculated t-statistic is 0.16 and the appropriate critical value for a two-tailed test with 18 degrees of freedom at α = 0.10 is 1.3368. Since the calculated t-statistic is less than the critical value, we fail to reject the null hypothesis. Therefore, we can conclude that there is no statistically significant difference in hold between the two brands.

Two Cosmetics Manufacturers Produce Similar Hairspray Products