Question

The mayor of a town has proposed a plan for the annexation of an adjoining community. A political study took a sample of 12001200 voters in the town and found that 75u% 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 above 72r%. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

The statistic for this test is given by:

`z=\frac{0.75 -0.72}{\sqrt{(0.72(1-0.72))/(1200)}}=2.31`

Explanation:

Information given

n=1200 represent the random sample taken

`\hat p=0.75` estimated proportion of residents who favored annexation.

`p_o=0.72` is the value that we want to test

z would represent the statistic

System of hypothesis

we want to test if the percentage of residents who favor annexation is above 72%, so then the system of hypothesis are:

Null hypothesis:
`p\leq 0.72`

Alternative hypothesis:
`p > 0.72`

The statistic for this case is given from the one sample proportion test:

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

Replacing the info given we got:

`z=\frac{0.75 -0.72}{\sqrt{(0.72(1-0.72))/(1200)}}=2.31`