Political Pollsters contacted 500 people in a city of 200,000 to determine the p
ID: 3218474 • Letter: P
Question
Political Pollsters contacted 500 people in a city of 200,000 to determine the percent of people who plan to vote for candidate "A". If the candidate receives 40% of the votes, the pollsters will recommend that he will continue his campaign. If 175 people indicate that they will vote for candidate "A", what should the pollsters recommend?
a. Show your check of all assumptions and conditions before beginning the problem.
b. Create a 90% confidence interval for the percentage of people who plan to vote for candidate "A". Include your Minitab output.
c. Explain what a 90% confidence interval means in general and in relationship to this problem.
d. What should the pollsters recommend? Support your answer.
Explanation / Answer
here as n/N<0.5 also np(1-p)>!0 hence we can apply normal approximation here
b)p=175/500=0.35 ; n=500
std error =(p(1-p)/n)1/2 =0.0213
for 90% CI, z=1.6449
hence confidence interval =sample proportion -/+ z*std error =0.3082 ; 0.3918
c)above confidence itnerval provide 90% probability to contain true mean of proportion who voted for candidate A
d)as above interval does not contain 40% as possible value, pollsters should tell him to discontinue his campaign