Question

The news program wishes to test whether there is evidence that more than three-quarters of U.S. adults are opposed to the verdict. Five hundred and sixty-two partici- pants participated in the survey, of which 82% said that they were unhappy with the verdict. a. State the null and alternative hypotheses for this test. b. What is the value of the statistic

Answer 1

Answer:

A)Null Hypothesis; H0: p ≤ 0.75

Alternative Hypothesis; Ha: p > 0.75

B) Test statistic is z = 3.83

Step-by-step explanation:

We are told the news program wants to test whether there is evidence that more than three - quarters of U.S. adults are opposed to the verdict.

Thus, p = 3/4 = 0.75

Thus,the hypothesis is;

Null Hypothesis; H0: p ≤ 0.75

Alternative Hypothesis; Ha: p > 0.75

Also, from a sample of Five hundred and sixty - two participants that participated in the survey, 82% said that they were unhappy with the verdict.

Thus; p^ = 82% = 0.82 and n = 562

Population standard deviation is given by the formula;

σ_p = √(p(1 - p)/n)

σ_p = √(0.75(1 - 0.75)/562)

σ_p = 0.0183

Now, the formula for the test statistic is;

z = (p^ - p)/σ_p

z = (0.82 - 0.75)/0.0183

z = 3.83