A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 points, and their standard deviation is 21.4 points. a. Find a 95% confidence interval for the mean score on the test. Be sure to write out what you entered in your calculator. (3 points) b. Interpret the interval you found in part a. (2 points) For parts c-e, calculations are not necessary. Deduce the answer from your knowledge of confidence intervals. c. Suppose the standard deviation of the tests had been 42.8 points instead of 21.4 points. What would the larger standard deviation do to the width of the confidence interval? (1 point) d. If the confidence level were reduced to 90%, will the interval be wider or narrower? (1 point) e. If the sample size was increased to 75 subjects, will the interval be wider or narrower? (1 point)