Answer:
The value of the test statistic is 2.17.
Step-by-step explanation:
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the hypothetised mean, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 54%.
This means that:
[tex]\mu = 0.54[/tex]
[tex]\sigma = \sqrt{0.54*0.46} = 0.4984[/tex]
A political study took a sample of 1300 voters in the town and found that 57% of the residents favored construction.
This means that [tex]n = 1300, X = 0.57[/tex]
Find the value of the test statistic.
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{0.57 - 0.54}{\frac{0.4984}{\sqrt{1300}}}[/tex]
[tex]t = 2.17[/tex]
The value of the test statistic is 2.17.
