Final answer:
This is a one-tailed test with a significance level of 0.08. The null hypothesis is rejected based on the test statistic and the decision rule. The p-value represents the probability of observing a difference in means as extreme as the observed difference, assuming the null hypothesis is true.
Step-by-step explanation:
a. This is a one-tailed test because the alternative hypothesis specifies a direction (μ1 > μ2).
b. The decision rule depends on the significance level. Since the significance level is 0.08, we compare the p-value to 0.08. If the p-value is less than 0.08, we reject the null hypothesis.
c. To compute the test statistic, we first calculate the standard error of the difference in means using the formula: SE = sqrt((s1^2/n1) + (s2^2/n2)), where s1 and s2 are the sample standard deviations and n1 and n2 are the sample sizes. Then, we calculate the test statistic as: test_statistic = (sample_mean1 - sample_mean2) / SE.
d. Based on the test statistic and the decision rule, we reject the null hypothesis (H0 : μ1 ≤ μ2).
e. The p-value is the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true. We can find the p-value by comparing the test statistic to a t-distribution with degrees of freedom equal to the sum of the sample sizes minus 2.