Question

The mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 1300 voters in the town and found that 57% 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 54%. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

The value of the test statistic is 2.17.

Explanation:

The test statistic is:

`t = (X - \mu)/((\sigma)/(√(n)))`

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

Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 54%.

This means that:

`\mu = 0.54`

`\sigma = √(0.54*0.46) = 0.4984`

A political study took a sample of 1300 voters in the town and found that 57% of the residents favored construction.

This means that
`n = 1300, X = 0.57`

Find the value of the test statistic.

`t = (X - \mu)/((\sigma)/(√(n)))`

`t = (0.57 - 0.54)/((0.4984)/(√(1300)))`

`t = 2.17`

The value of the test statistic is 2.17.