The YRBR (Youth Risk Behavior Survey) asked youth, "How many days (per month) were you physically active?" They found the sample mean, xbar = 3.8 days, and sample standard deviation, s= 2.6 days. Investigators wish to make inference to a mean, mu = population average days active (per month).

Suppose n= 100 students. [YRBS is much larger, but just suppose the n=100.] "Number of Days Physically Active" is not normally distributedin fact, it is strongly right-skewed.

Would we need the "days active" to be normally distributed" to be compute a "t" CI for the mean "Number of Days Physically Active"?

a.No, because t confidence procedures are nonparametric.

b. No, because the sample size (n=100) is sufficiently large and t procedures are robust.

c. Yes, because normality is an assumption for t confidence intervals.

d. No, because we can use a Wilcoxon rank-sum confidence interval for the mean here.