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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 m1 and process 2 has a mean defined as m2. The null and alternative hypotheses are as follows:

H0: µ1 – µ2 ≥ 0

H1: µ1 – µ2 < 0

Using a random sample of 25 paired observations, the standard deviation of the difference between sample means is 25. Can you reject the null hypothesis using a probability of Type I error a = 0.05 in each case?

a. The sample means are 56 and 50

b. The sample means are 59 and 50

c. The sample means are 56 and 48

d. The sample means are 54 and 50

H0: µ1 – µ2 ≥ 0

H1: µ1 – µ2 < 0

Using a random sample of 25 paired observations, the standard deviation of the difference between sample means is 25. Can you reject the null hypothesis using a probability of Type I error a = 0.05 in each case?

a. The sample means are 56 and 50

b. The sample means are 59 and 50

c. The sample means are 56 and 48

d. The sample means are 54 and 50

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