Question

calculate the test statistic.
a research company claims that no more than 55% of americans regularly watch fox news. you decide to test this claim and ask a random sample of 425 americans if they watch this network regularly. of the 425 sampled, 255 respond yes. calculate the test statistic for the hypothesis test.
-2.07
1.645
-1.96
2.07
none of the above.

Explanation:

Step1: Calculate sample proportion

The sample proportion \( \hat{p}=\frac{255}{425} = 0.6\)

Step2: Set up hypothesis

The null hypothesis \(H_0:p\leq0.55\) and the alternative hypothesis \(H_1:p > 0.55\)

Step3: Calculate test statistic

The formula for the z - test statistic for a proportion is \(z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}\)
Substitute \(p = 0.55\), \(\hat{p}=0.6\), and \(n = 425\)

$$
LATEXBLOCK0
$$

Answer:

2.07