Q1. A sample of 65 observations is selected from one population with a population standard deviation of 0.75. The sample mean is 2.67. A sample of 50 observations is selected from a second population with a population standard deviation of 0.66. The sample mean is 2.59. Conduct the following test of hypothesis using the .08 significance level.
H0 : μ1 - μ2 ≤ 0
H1 : μ1 - μ2 > 0
a. Is this a one-tailed or two-tailed test?
b. State the decision rule.
c. Compute the value of the test statistic.
d. What is your decision regarding H0?
e. What is the p-value? Interpret the p-value.
Q2. The null and alternative hypotheses are:
H0 : P1 - P2 = 0
H1 : P1 - P2 ≠0
A sample of 200 observations from the first population indicated that X1 is 170. A sample of 150 observations from the second population revealed X2 to be 110. Use the .05 significance level to test the hypothesis.
a. State the decision rule.
b. Compute the pooled proportion.
c. Compute the vale of the test statistic.
d. What is your decision regarding the null hypothesis?
e. Determine and interpret the p-value.