Question

A publisher reports that 52% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 180 found that 46% of the readers owned a laptop. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

Answer:

The value of the test statistic is $t = -1.61$

Step-by-step explanation:

Central Limit Theorem

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Our test statistic is:

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

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

A publisher reports that 52% of their readers own a laptop.

This means that $\mu = 0.52$

Sample of 180:

Means that $n = 180$

By the Central Limit Theorem:

$\frac{\sigma}{\sqrt{n}} = s = \sqrt{\frac{0.52*0.48}{180}} = 0.0372$

A random sample of 180 found that 46% of the readers owned a laptop.

This means that $X = 0.46$

Find the value of the test statistic.

$t = \frac{X - \mu}{s}$

$t = \frac{0.46 - 0.52}{0.0372}$

$t = -1.61$

The value of the test statistic is $t = -1.61$