Question

A market research analyst claims that 32% of the people who visit the mall actually make a purchase. You think that less than 32% buy something and decide to test the claim. You stand by the exit door of the mall starting at noon and ask 82 people as they are leaving whether they bought anything. You find that only 20 people made a purchase. The value of the test statistic is about:
A. 1.74
B. 1.60
C. 1.48
D. -1.60
E. -1.48

Answer 1

Answer:

E. -1.48

Step-by-step explanation:

The test statistic is:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the expected value, $\sigma$ is the standard deviation and n is the size of the sample.

A market research analyst claims that 32% of the people who visit the mall actually make a purchase.

This means that:

$\mu = 0.32$

$\sigma = \sqrt{0.32*0.68} = 0.4665$

You stand by the exit door of the mall starting at noon and ask 82 people as they are leaving whether they bought anything. You find that only 20 people made a purchase.

This means that $n = 82, X = \frac{20}{82} = 0.2439$

The value of the test statistic is about:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$t = \frac{0.2439 - 0.32}{\frac{0.4665}{\sqrt{82}}}$

$t = -1.48$

So the correct answer is given by option E.