Question

The mayor of a town has proposed a plan for the annexation of an adjoining community. A political study took a sample of 900 voters in the town and found that 37% 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 more than 33%. Find the value of the test statistic. Round your answer to two decimal places

Answer 1

The value of the test statistic is 2.49

Explanation:

We are given the following in the question:

Sample size, n = 900

p = 33% = 0.33

Sample proportion of the residents favored annexation = 37%

First, we design the null and the alternate hypothesis

`H_(0): p = 33\\H_A: p > 0.33`

This is a one-tailed(right) test.

Formula:

`\hat{p} = 0.37`

`z = \frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}`

Putting the values, we get,

`z = \displaystyle\frac{0.37-0.33}{\sqrt{(0.37(1-0.37))/(900)}} = 2.4854\approx 2.49`

Thus, the value of the test statistic is 2.49