Respuesta :
Answer:
The value of the test statistic is 2.47.
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 expected mean, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
For a proportion p, we have that:
[tex]s = \frac{\sigma}{\sqrt{n}} = \sqrt{\frac{p(1-p)}{n}}[/tex]
A political study took a sample of 900 voters in the town and found that 42% of the residents favored annexation.
This means that [tex]X = 0.42, n = 900[/tex]
Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is above 38%
This means that the expected is [tex]\mu = p = 0.38[/tex]
So
[tex]s = \frac{\sigma}{\sqrt{n}} = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.38*0.62}{900}} = 0.0162[/tex]
Find the value of the test statistic
[tex]t = \frac{X - \mu}{s}[/tex]
[tex]t = \frac{0.42 - 0.38}{0.0162}[/tex]
[tex]t = 2.47[/tex]
The value of the test statistic is 2.47.
