Question

According the a University Center for Logistics Management, 7% of all merchandise sold in the United States gets returned. A Seattle department store samples 89 items sold in January and found that 10 of the items were returned. H0: p = 0.07 H1: p < 0.07 Calculate the test statistic: Group of answer choices 1.31 2.33 0.99 1.15 1.57

Answer 1

The test statistic is 1.57.

Explanation:

Our test statistic is:

`t = (X - \mu)/((\sigma)/(√(n)))`

In which X is the sample mean,
`\mu` is the value tested at the null hypothesis,
`\sigma` is the standard deviation and n is the size of the sample.

A Seattle department store samples 89 items sold in January and found that 10 of the items were returned.

This means that
`n = 89, X = (10)/(89) = 0.1124`

7% of all merchandise sold in the United States gets returned.

This means that
`\mu = 0.07`

For a proportion, the standard deviation is
`\sigma = √(p(1-p)) = √(0.07*(1-0.07)) = 0.2551`

Test statistic:

`t = (X - \mu)/((\sigma)/(√(n)))`

`t = (0.1124 - 0.07)/((0.2551)/(√(89)))`

`t = 1.57`

The test statistic is 1.57.