Question

ESSAY. Write your answer in the space provided or on a separate sheet of paper. Provide an appropriate response. (11) A mayoral election race is tightly contested. In a random sample of 2000 likely voters, 1045 said that they were planning to vote for the current mayor. Based on this sample, would you claim and tell the mayor, that they will absolutely win a majority of the votes? Calculate and explain your answer and then also discuss how the answer could be different (opts) (Calculate 2 confidence intervals and discuss how they could give views of the election)

Answer 1

Here were testing Hoi P=0.5 rs Ha:P>0.5 lif. this is one-tailed test. the test statistic is given by 2= P-0.5 which follows a standard normal - Vosxo-s/2000 under Ho. here P = lous, the sample proportion = 0.5225 hence the test statistic is 2.010 : and the p value is P( 272.01) - 0.0221 Hence if level of test is a=o.os then we reject the null hypothesis thoole. we conclude that there s signienough evidence to support the claim that present will have the majority. While if a 2001, then we fail to reject Ho. Similarly we can calculate the a confidence intervals. ast. Confidence interval => kan I 1960.stos = (0.5006, 10.5444) hence this doesn't contains o. and 90% Confidence interval is + 2.576.) 0:56805 - 10.4937, 0.5513) which contains o.s