1. An investigation is conducted to determine if the mean age of welfare recipients differs between two cities A and B. Random samples of 60 and 40 welfare recipients are selected from city A and city B, respectively, the following computations are made.

City A (population 1 ) City B (population 2 )

Mean 35.8 42.2

Standard Deviation 3.8 4.5

Do the data provide strong evidence that the mean ages are difference in city A and city B?

(3 State the null hypothesis and alternative hypothesis

(b) Find the test statistic

(c) If the type-I error = 0.05, find the critical value(s) and shade the rejection region(s)

(d) Base on the type-I error and rejection region(s), given above, what is your conclusion?

2. To evaluate the effectiveness of a new pain relief drug, an experiment was conducted in which 14 subjects received the new drug (population 1) and 15 subjects received the old one (population 2). Among the subjects receiving the new drug, the pain disappeared in 16.6 minutes on the average with a standard deviation of 20.4 min. Among the subject receiving the old one,the pain disappeared in 22.4 minutes on the average with a standard deviation of 14.8 min. Test if the new drug relief pain faster than the old one. Assume that the population variances are unequal and unknown.

(a) State the null hypothesis and alternative hypothesis

(b) Find the test statistic

(c) If the type-I error = 0.05, find the critical value(s) and shade the rejection region(s)

(d) Base on the type-I error and rejection region(s), given above, what is your conclusion?

3. The auto insurance agent claims that, on the average, the number of cars stolen in the Bronx is greater than the number in Manhattan. A NY state assemblyman obtained the following data on car thefts from NYC police records. The number of cars stolen each month for the last 6 months in the two boroughs are as follows.

Bronx (population 1) 11 20 18 17 22 30

Manhattan (population 2) 15 12 14 18 17 15

Assume that the population variances are equal but unknown. Test the insurance agent's claim.

(a) State the null hypothesis and alternative hypothesis

(b) Find the test statistics

c) If the type-I error = 0.05, find the critical value(s) and shade the rejection region(s)

(d) Base on the type-I error and rejection region(s), given above, what is your conclusion?