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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

Respuesta :

Answer:

The value of the test statistic is 2.49              

Step-by-step 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  

[tex]H_{0}: p = 33\\H_A: p > 0.33[/tex]

This is a one-tailed(right) test.  

Formula:

[tex]\hat{p} = 0.37[/tex]

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

Putting the values, we get,

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

Thus, the value of the test statistic is 2.49

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