MATH 100 ELEMENTARY PROBATILITY AND STATISTICS EXAM 2 IA. A sample of 21 first year night-school students' ages is obtained in order to estimate the mean age of night school students. The study yielded the sample mean of x 24.5 years, Assume that the age of the night-school students is normally distributed with the standard deviation of 16.7. (a) Which approximation is more appropriate in this problem, % or t? Be sure to justify your rouponse . (5 points) (b) Estimate the 95% confidence interval of the mean age. Be sure to justify all steps graphically and analytically. (10 points)

1B. Does the sample study of Problem 1A yield sufficient evidence to declare the mean age of the first year night students exceed 23.0?
(c) Set up the appropriate hypotheses. (5 points)
(d) Test the hypotheses with the significance level of a = 0.05. Be sure to justify all steps graphically and analytically. (10 points)