Question

A factory compares samples of well-produced widgets and defects from two manufacturing plants:

                        Plant 1             Plant 2

Good               600                450

Defect                40                    50

Use a hypothesis test at 95% to determine if the plants are not performing the manufacturing process with similar success.

Answer 1

Here we need to compare two proportions so z test for comparing proportions will be used.

Here the claim (alternative hypothesis) is

So test is two tailed. Following is the null hypothesis:

Here we have

Pooled sample proportion is

Standard error of the test is:

So test statistics will be

The p-value is:

p-value = 0.0198

Excel function used for p-value: "=2*(1-NORMSDIST(2.33))"

Since p-value is less than 0.05 so we reject the null hypothesis.

That is we can conclude that the plants are not performing the manufacturing process with similar success.