The authors of the paper ?Sex Differences in Time Perception During Smoking Abstinence? (Nicotine and Tobacco Research [2015]: 449?454) investigated how nicotine withdrawal affects time perception and decision making. In this study, 21 male smokers were asked to abstain from smoking for 24 hours. After 24 hours, they were shown a demo screen with a green cross that changed to a red cross after a period of time. They were then shown a green cross and asked to indicate when they thought the same amount of time had passed as in the demo. This process was repeated 15 more times with varying times. A time discrimination score was calculated for each man by dividing the total of the estimated times by the total of the actual times. Suppose that the 21 time discrimination scores were the ones shown below. These values are consistent with summary values given in the paper.

a. What characteristic of the sample size indicates that the methods based on the t distribution may not be appropriate?

b. Use the given Shiny app output to estimate the mean time discrimination score for the population of male smokers who abstain from smoking for 24 hours using a 95% confidence interval.

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1.12 1.03 1.09 1.03 1.09 0.97 0.98 1.20 1.16 1.03 1.10 1.11 0.98 1.02 120 0.96 0.78 1.05 090 1.08 0.95