Independent random samples were selected from two I normally distributed populations with means p, and p2, respectively. The sample sizes, means, and variI ances are shown in the followmg table.

I

..............................................

Sample 1 Sample 2 .........................................

n1 = 12 - n2 = 14 -

x1 = 17.8 x, = 15.3 sf = 74.2 s; = 60.5

a. Test H,: (pl - p2) = 0 against Ha: (p, - p2) > 0.

Use a = .05.

b. Form a 99% confidence interval for (p, - p2).

c. How large must n, and n2 be if you wish to estimate (pl - p2) to within 2 units with 99% confidence? Assume that n1 = n2.

+7.90 Two independent random samples were selected from normally distributed populations with means and variances (pl, uf) and (p,, u;), respectively. The sample sizes, means, and variances are shown in the table below.

Sample 1 Sample 2 ...............................................

n, = 20 n2 = 15 -

x1 = 123 & = 116 sf = 31.3 sz = 120.1

a. Test H,: a: = a$ against Ha: a: # a$. Use a = .05.

b. Would you be willing to use a t-test to test the null hypothesis H,: (p, - p2) = 0 against the alternative hypothesis Ha: (p, - p2) # O? Why?