Question

A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a simple random sample of n = 1100 registered voters and found that 570 of those voters would vote for the Republican candidate. Let p represent the proportion of all registered voters in the state who would vote for the Republican candidate. We test the following hypotheses using a significance level of α = 0.05:

H0 : p = 0.50

Ha : p > 0.50

(a) Calculate the proportion of all registered voters from the sample who would vote for the Republican candidate. Round your answer to two decimal places.

(b) Calculate the z-test statistic for the hypothesis test. Round your answer to two decimal places.

(c) Calculate the p-value of the test. Round your answer to two decimal places. Be sure to show how you obtained this value.

(d) Based on your p-value, do you reject or fail to reject the null hypothesis? Explain your answer.

(e) How do we conclude? Circle the letter (A, B, C, or D) that represents your answer.

A. We have sufficient evidence to suggest that most of the registered voters in the state would vote for the Republican candidate.

B. We do not have sufficient evidence to suggest that most of the registered voters in the state would vote for the Republican candidate.

C. We have sufficient evidence to suggest that most of the registered voters in the state would not vote for the Republican candidate.

D. We have sufficient evidence to suggest that exactly half of the registered voters in the state would vote for the Republican candidate.

Answer 1