Question

Fred Schwartz is running for public office and his campaign manager is hoping to estimate the proportion of registered voters that will vote for Mr. Schwartz. In a Gallup poll of 1501 registered voters, 345 indicated that they will vote for Mr. Fred Schwartz.

a) Based upon this sample, what is the point estimate for the proportion of registered voters that will vote for Mr. Fred Schwartz? the point estimate for the proportion:_____________________________

b) Using this Gallup poll, compute the 98% confidence interval for the proportion of registered votes that will vote for Mr. Fred Schwartz. 98% confidence interval :_________________________________________

c) Based upon this interval estimate, should the campaign manager conclude with confidence that the majority of registered voters will vote for Mr. Fred Schwartz? Explain your answer.

Answer 1

a)

Sample proportion = 345 / 1501 = 0.230

Point estimate for proportion = = 0.230

b)

p̂ ± Z(α/2) √( (p * q) / n)
0.2298 ± Z(0.02/2) √( (0.2298 * 0.7702) / 1501)
Z(α/2) = Z(0.02/2) = 2.326
Lower Limit = 0.23 - Z(0.02) √( (0.2298 * 0.7702) / 1501) = 0.205
upper Limit = 0.23 + Z(0.02) √( (0.2298 * 0.7702) / 1501) = 0.255
98% Confidence interval is ( 0.205 , 0.255 )

c)

Since all values in confidence interval are less than 0.50,

We do not have sufficient evidence to support the claim that majority of registered voters will vote for Mr. Fred Schwartz