Question

The mayor of a town has proposed a plan for the annexation of a new community. A political study took a sample of 900900 voters in the town and found that 42B% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is above 388%. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

The value of the test statistic is 2.47.

Explanation:

The test statistic is:

`t = (X - \mu)/((\sigma)/(√(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.

For a proportion p, we have that:

`s = (\sigma)/(√(n)) = \sqrt{(p(1-p))/(n)}`

A political study took a sample of 900 voters in the town and found that 42% of the residents favored annexation.

This means that
`X = 0.42, n = 900`

Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is above 38%

This means that the expected is
`\mu = p = 0.38`

So

`s = (\sigma)/(√(n)) = \sqrt{(p(1-p))/(n)} = \sqrt{(0.38*0.62)/(900)} = 0.0162`

Find the value of the test statistic

`t = (X - \mu)/(s)`

`t = (0.42 - 0.38)/(0.0162)`

`t = 2.47`

The value of the test statistic is 2.47.