1. Given the following information about a hypothesis test of comparing the two variances based on independent random samples, what is the critical value of the test statistic at a significance level of .05? Assume that the samples are obtained from normally distributed populations having equal variances. H0: A = B
H1: A > B
X ¯ 1 = 12
X ¯ 2 = 9
s1 = 4
s2 = 2
n1 = 13
n2 = 10
A. Reject H0 if Z > 1.96
B. Reject H0 if Z > 1.645
C. Reject H0 if t > 2.08
D. Reject H0 if t > 1.782
E. Reject H0 if t > 1.721
2. Given the following information about a hypothesis test of the difference between two means based on independent random samples, what is the standard deviation of the difference between the two means? Assume that the samples are obtained from normally distributed populations having equal variances.
H0: A = B
H1: A > B
X ¯ 1 = 12
X ¯ 2 = 9
s1= 5
s2 = 3
n1 =13
n2 =10
A. 1.792
B. 1.679
C. 2.823
D. 3.210
E. 1.478