Question

The mayor of a town has proposed a plan for the construction of a new community. A political study took a sample of 1300 voters in the town and found that 45% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 42%. 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 = 2.19.

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.

Sample of 1300 voters:

This means that $n = 1300$

Found that 45% of the residents favored construction.

This means that $X = 0.45$

A political strategist wants to test the claim that the percentage of residents who favor construction is more than 42%.

This means that $\mu = 0.42$, and by the Central Limit Theorem:

$\frac{\sigma}{\sqrt{n}} = s = \sqrt{\frac{0.42*0.58}{1300}} = 0.0137$

So, the test statistic is:

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

$t = \frac{0.45 - 0.42}{0.0137}$

$t = 2.19$

The value of the test statistic is t = 2.19.