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 mu 1 and process 2 has a mean defined as mu 2. the null and alternative hypotheses are
h 0: mu 1-mu 2≤0
and
h 1 : mu 1 - mu 2 > 0.
the process variances are unknown but assumed to be equal.
using random samples of 36 observations from process 1 and 25 observations from process 2, the sample means are 55 and 50 for populations 1 and 2 respectively. complete parts a through d below.
a. can you reject the null hypothesis, using a probability of type i error α =0.05, if the sample standard deviation from process 1 is 31 and from process 2 is 28?
b. can you reject the null hypothesis, using a probability of type l error α=0.05, if the sample standard deviation from process 1 is 21 and from process 2 is 31?
c. can you reject the null hypothesis, using a probability of type i error α =0.05, if the sample standard deviation from proces 1 is 28 and from proces 2 is 31?
d. can you reject the null hypothesis, using a probability of type i error α =0.05, if the sample standard deviation from proces 1 is 14 and from proces 2 is 43?