Question

An ACME Bearings manager wants to compare the average ball bearing size from two different machines. She suspects the mean diameter for bearing from machine 2 exceeds that of bearings from machine 1. She takes two independent, random samples of size 50, one from each machine. The mean and standard deviation of bearings taken from machine 1 are 3.302 mm and 0.051 mm. The mean and standard deviation of bearings taken from machine 2 are 3.355 mm and 0.050 mm. Run a hypothesis test consistent with her suspicions. Be sure to

a. check all necessary assumptions

(Independent random samples, large enough sample size- it will follow the normal distribution, both s.d is almost same.)

b. state the null and alternative hypotheses

H0 : mu2-mu1=0

Ha : mu2-mu1>0

I think mu2 - mu1 >0 because her suspect is that machine 2 exceeds that of from machine 1. However every answer is opposite such as mu2-mu1<0.

Would you please explain it?

c. calculate the test statistic and p-value

why we have to use the t-test instead of z-test?

d. state your conclusion in a complete sentence based of the p-value.

Answer 1