Answer:
The test statistic is 1.57.
Step-by-step explanation:
Our test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] 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 [tex]n = 89, X = \frac{10}{89} = 0.1124[/tex]
7% of all merchandise sold in the United States gets returned.
This means that [tex]\mu = 0.07[/tex]
For a proportion, the standard deviation is [tex]\sigma = \sqrt{p(1-p)} = \sqrt{0.07*(1-0.07)} = 0.2551[/tex]
Test statistic:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{0.1124 - 0.07}{\frac{0.2551}{\sqrt{89}}}[/tex]
[tex]t = 1.57[/tex]
The test statistic is 1.57.
