Question: A politician claims that she will receive 61% of the vote in an upcoming election. The results of a properly designed random sample of 100 voters showed that 49 of those sampled will vote for her. Is it likely that her assertion is correct at the 0.05 level of significance?

(a) State the appropriate null and alternative hypotheses.

Ho: p 0.61

Ha: p 0.61

(ii) Find z. (Give your answer correct to two decimal places.)

(iii) Find the p-value. (Give your answer correct to four decimal places.)

(b) State the appropriate conclusion.

Reject the null hypothesis, there is not significant evidence that she will receive less than 61% of the vote.

Reject the null hypothesis, there is significant evidence that she will receive less than 61% of the vote. Fail to reject the null hypothesis, there is not significant evidence that she will receive less than 61% of the vote.

Fail to reject the null hypothesis, there is significant evidence that she will receive less than 61% of the vote.