9.49 A single-sample t test and Victoria’s Secret perfume as an insect repellent: Biology researchers examined the mosquitorepelling effects of a control (no scent), insect repellents that contain DEET, natural insect repellents, and several beauty products (Rodriguez et al., 2015). In the control condition, on average, 61% of a swarm of mosquitoes chose to enter a chamber with a hand in it. For the purposes of this exercise, we’ll treat this as the population mean. When the hand was sprayed with a high concentration of Victoria’s Secret Bombshell perfume, only 17% of mosquitoes entered the chamber on average. The standard deviation for the sample of five perfumed hands was 12.052. (Interestingly, the perfume was almost as effective as bug spray with DEET; for example, Cutter Skinsations had a mean of 11%.

The perfume worked better than Cutter’s natural bug spray, which had a mean of 57% and better than the bug spray based on Avon’s Skin So Soft lotion, a long-heralded home remedy, which had a mean of 48%.)

a. Explain why a single-sample t test is the appropriate hypothesis test to examine the effect of the perfume against the control.

b. Conduct all six steps of hypothesis testing for the effect of the perfume against the control.

c. Calculate the effect size for this hypothesis test. According to Cohen’s conventions, how large is this effect?

d. Calculate the confidence interval for the sample mean for the perfume.

e. Explain how the confidence interval gives us the same information as the hypothesis test.

f. If you rejected the null hypothesis, how might replication help to determine whether these findings might be a Type I error? g. If researchers attempted to replicate this study in a different laboratory in a different part of the world and failed to replicate it, explain why, other than a Type I error, this failure might have occurred.