Question

Suppose Harvey owns a small business that produces electron microscopes. He previously owned one machine, machine A, that produced these microscopes. In an effort to increase production, he recently purchased a new machine, machine B, that also produces microscopes. Although both machines produce microscopes at the same rate, Harvey suspects that machine A produces more defective microscopes than machine B. In order to test this hypothesis, he randomly selects 300 microscopes produced by machine A and 280 microscopes produced by machine B. He observes that 18 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 greater than the frequency of defective items produced by machine B. Select the appropriate test that Harvey should perform to test his hypothesis. matched-pairs ????t ‑test two-sample ????z ‑test for two proportions one-sample ????z ‑test for a mean two-sample ????t ‑test for two means one-sample ????z ‑test for a proportion

Answer 1

Explanation:

Given that Harvey owned one machine, machine A, that produced these microscopes. In an effort to increase production, he recently purchased a new machine, machine B, that also produces microscopes.

We have to compare the proportion of defective microscopes of A and B and check whether that of A > that of B.

This is a hypothesis testing for comparison of two proportions.

Here only sample std deviation is known and hence t test should be used.

t ‑test two-sample proportions