Question

A company wants to examine the average operation time for a process. Two methods were used. A random sample of 40 for the first method gives an average mean time of 20.5 minutes with variance of 3 minutes. A random sample of 50 for the second method gives an average mean time of 17.6 minutes with variance of 4 minutes. (Use normal distribution with variance known)

1. Determine the 95% confidence interval for the difference between the means
2. At alpha =0.05 can we conclude that there is a difference in the mean times? (Hypothesis test)

Answer 1

a) 95% confidence interval for the difference between the means

is 95% confidence interval for the difference between the means.

b) NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

alpha=0.05

Z critical=1.96

Since Z cal is greater than Z critical therefore we reject null hypothesis H0 and conclude that there is difference in mean times.