About 30% of people cannot detect any odor when they sniff the steroid adrostenone, but they can become sensitive to its smell if exposed to the chemical repeatedly. Does this change in sensitivity happen in the nose or in the brain? Maninland et al. (2002) exposed one nostril of each of 12 non-detector participants to androstenone for short periods every day for 21 days. The other nostril was plugged and had humidified air flow to prevent androstenone from entering. After the 21 days, the researchers found that 10 of 12 participants had improved androstenone-detection accuracy in the plugged nostril, whereas two had reduced accuracy. This suggested that increases in sensitivity to androsternone happen in the brain rather than the nostril, since the epithelia of the nostrils are not connected. The authors conducted a statistical hypothesis test of whether accuracy in fact did change. Let p refer to the proportion of non-detectors in the population whose accuracy scores improve after 21 days. Under the null hypothesis, p=0.5 (as many participants should improve as deteriorate in their accuracy after 21 days.)

a. Did the authors carry out a one- or two- sided test? What justification might they provide?

b. What is the test statistic for the test?

c. What is the p-value for the test?

d. What is the appropriate conclusion? Use significance level α = 0.05