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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

User Mmcorrelo
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1 Answer

2 votes

Answer:

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.

User Nuriel
by
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