Question

Suppose Harvey owns a small business that produces computer motherboards. He previously owned one machine, machine A, that produced these motherboards. In an effort to increase production, he recently purchased a new machine, machine B, that also produces motherboards. Although both machines produce motherboards at the same rate, Harvey suspects that machine A produces fewer defective motherboards than machine B. In order to test this hypothesis, he randomly selects 260 motherboards produced by machine A and 200 motherboards produced by machine B. He observes that 13 of the sampled items from machine A are defective and 14 sampled items from machine B are defective. Harvey plans to use the sample data he collected to test if the frequency of defective items produced by machine A is less than the frequency of defective items produced by machine B.

Select the appropriate test that Harvey should perform to test his hypothesis.
a. two-sample t-test for two means
b. one-sample z-test for a mean
c. one-sample z-test for a proportion
d. matched-pairs t-test
e. two-sample z-test for two proportions

Answer 1

e. two-sample z-test for two proportions

Explanation:

He has two machines, which have a proportion of defective motherboards. He want to compare this two proportions.

He takes two samples, one for each machine, and calculate the proportion in order to statistically test if there are significant difference between the proportions.

Then, this is a two-sample z-test for two proportions