In: Statistics and Probability
3. Suppose that you are working for a watch company studying the average wrist sizes of people in the population of the United States.
(a) If you are told that we know from previous studies that the standard deviation in women’s wrist sizes is 0.5 inches, and from a random sample of 20 women, the sample mean wrist size was 7.2 inches, create a 95% confidence interval for the true mean wrist size.
(b) Your boss comes back and tells you that they found out that the sample actually had 30 women, but everything else was correct. Create a new 95% confidence interval based on this information.
(c) Your boss comes back and tells you that they made a mistake and the 0.5 inch standard deviation was actually just the sample standard deviation and we don’t know the true value. In addition, it turns out there were only 10 women in the study. After calming down, create a new 95% confidence interval based on this information.