Question

A particular poll tracks daily the percentage of citizens from a certain country who approve or disapprove of the job the President is doing. Daily results are based on telephone interviews with approximately 1400 national adults. The poll reported that 50​% of adults approve of the President doing his job. A media outlet claimed the true proportion to be 52​%. Does the poll contradict this​ claim? Complete parts a through c. ​a) Test the appropriate hypothesis. Find a 95​% confidence interval for the sample proportion of adults in the country who approved of the​ President's performance. Check conditions. Which conditions for the confidence interval have been​ met? Select all that apply. A. ​Success/Failure Condition B. ​10% Condition C. Randomization Condition Let p be the proportion of adults in the country who approved of the​ President's performance. What are the null and alternative​ hypotheses? Upper H 0​: p ▼ greater than equals less than not equals nothing vs. Upper H Subscript Upper A​: p ▼ equals greater than less than not equals nothing ​(Type integers or decimals. Do not​ round.) Find the 95​% confidence interval. left parenthesis nothing comma nothing right parenthesis ​(Round to three decimal places as​ needed.) ​b) Does your confidence interval provide evidence to contradict the​ claim? Select the correct choice below and fill in the answer box to complete your choice. ​(Type an integer or a decimal. Do not​ round.) A. Since nothing is within the​ interval, the confidence interval does not provide evidence that contradicts the media​ outlet's claim. B. Since nothing is within the​ interval, the confidence interval provides evidence that contradicts the media​ outlet's claim. C. Since nothing is not within the​ interval, the confidence interval provides evidence that contradicts the media​ outlet's claim. D. Since nothing is not within the​ interval, the confidence interval does not provide evidence that contradicts the media​ outlet's claim. ​c) What is the significance level of the test in​ b? Explain. Select the correct choice below and fill in the answer box to complete your choice. ​(Type an integer or a decimal. Do not​ round.) A. The significance level is alphaequals nothing because the test is a​ two-tail test based on a 95​% confidence interval. B. The significance level is alphaequals nothing because the test is a​ one-tail test based on a 95​% confidence interval. C. The significance level is betaequals nothing because the test is a​ two-tail test based on a 95​% confidence interval. D. The significance level is betaequals nothing because the test is a​ one-tail test based on a 95​% confidence interval.

Answer 1

a)

A.​Success/Failure Condition B. ​10% Condition

Randomization condition may not satisfied because poll is based on telephone interview.

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b)

A. Since 0.52 is within the​ interval, the confidence interval does not provide evidence that contradicts the media​ outlet's claim.

c)

A. The significance level is alpha equals 0.05 because the test is a​ two-tail test based on a 95​% confidence interval.