3. The tolerable level of a certain pollutant is 16 mg/l. A researcher takes a sample of size n = 50, and finds that the mean level of the pollutant is 18.5 mg/l, with a standard deviation of 7 mg/l. Construct a 95% confidence interval around the sample mean, and determine whether the tolerable level is within this interval.

5. The proportion of people changing residence in the USA each year is 0.165. A researcher believes that the (> proportion may be different in the town of Amherst. She surveys 50 individuals in the town of Amherst and finds that the proportion who moved last year is 0.24. Is there evidence to conclude that the town has a mobility rate that is different from the national average? Use a = 0.05 and find a 90% confidence interval around the sample proportion, and state your conclusion.

7. A survey of the white and nonwhite population in a local area reveals the following annual trip frequencies to the nearest state park:
x, a 4.1. s, = 14.3. n, =20
x2 – 3.1, sf= 12.0. ^ = 16
where the subscript ‘ 1 ’ denotes the white population and the subscript ‘2’ denotes the nonwhite population.
a. Assume that the variances are equal, and test the null hypothesis that there is no difference between the park-going frequencies of whites and nonwhites.
b. Repeat the exercise, assuming that the variances are unequal.
c. Find the />-value associated with the tests in parts (a) and (b).
d. Associated with the test in part (a), find a 95% confidence interval for the difference in means.