The mayor of a town has proposed a plan for the annexation of a new community. A political study took a sample of 1300 voters in the town and found that 68% 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 65%. Testing at the 0.01 level, is there enough evidence to support the strategist's claim

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ChiKesselman ChiKesselman · Answer 1 · 2020-02-25T05:00:31+01:00

Answer:

There is not enough evidence to support the percentage of residents who favor annexation is more than 65%.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 1300

p = 65% = 0.65

Alpha, α = 0.01

First, we design the null and the alternate hypothesis

[tex]H_{0}: p = 0.65\\H_A: p > 0.65[/tex]

This is a one-tailed(right) test.

Formula:

[tex]\hat{p} = 68\% = 0.68[/tex]

[tex]z = \dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]

Putting the values, we get,

[tex]z = \displaystyle\frac{0.68-0.65}{\sqrt{\frac{0.65(1-0.65)}{1300}}} = 2.2678[/tex]

Now, we calculate the p-value from the table.

P-value = 0.011671

Since the p-value is greater than the significance level, we fail to reject the null hypothesis and accept the null hypothesis.

Thus, there is not enough evidence to support the percentage of residents who favor annexation is more than 65%.