Answer to Question #11235 in Statistics and Probability for Raghav Agrawal

Question

1. You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean defined as µ1 and process 2 has a mean defined as µ2. The null and alternative hypotheses are as follows:

Ho: µ1 - µ2 ≤ 0
H1: µ1 - µ2 > 0

The process variances are unknown but assumed to be equal. Using a random sample of 25 observations from process 1 and 36 observations from process 2, the sample means are 56 and 50 for populations 1 and 2. Can you reject the null hypothesis using a probability of Type I error α = 0.05 if

a. The sample standard deviation from process 1 is 30 and from process 2 is 28?
b. The sample standard deviation from process 1 is 22 and from process 2 is 33?
c. The sample standard deviation from process 1 is 30 and from process 2 is 42?
d. The sample standard deviation from process 1 is 15 and from process 2 is 36?