Question

The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 900 voters in the town and found that 63% 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 over 59%. Make the decision to reject or fail to reject the null hypothesis at the 0.02 level

Answer 1

Using the z-distribution, it is found that since the p-value is less than 0.02, we reject the null hypothesis.

What are the hypothesis tested?

At the null hypothesis, it is tested if the proportion is of at most 59%, that is:

$H_0: p \leq 0.59$

At the alternative hypothesis, it is tested if the proportion is greater than 59%, hence:

$H_1: p > 0.59$

What is the test statistic?

The test statistic is given by:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$

In which:

• $\overline{p}$ is the sample proportion.

• p is the proportion tested at the null hypothesis.

• n is the sample size.

For this problem, the parameters are:

$p = 0.59, n = 900, \overline{p} = 0.63$

Hence the value of the test statistic is found as follows:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$

$z = \frac{0.63 - 0.59}{\sqrt{\frac{0.59(0.41)}{900}}}$

z = 2.44.

What is the p-value and the conclusion?

Using a z-distribution calculator, for a right-tailed test, as we are testing if the proportion is higher than a value, with z = 2.44, the p-value is of 0.0073.

Since the p-value is less than 0.02, we reject the null hypothesis.

More can be learned about the z-distribution at https://brainly.com/question/16313918

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