Two Cosmetics Manufacturers Produce Similar Hairspray Products

Multiple Choice

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) .

A) CV = 1.3368; TS = 0.16; reject H₀; Conclusion: There exists a statistically significant difference in hold.
B) CV = 1.3304; TS = -0.23; fail to reject H₀; Conclusion: There is no statistically significant difference in hold.
C) CV = -2.5835; TS = 0.23; reject H₀; Conclusion: There exists a statistically significant difference in hold.
D) CV = 1.3368; TS = 0.16; fail to reject H₀; Conclusion: There is no statistically significant difference in hold.