Question

A simple random sample of 1500 registered voters was surveyed and asked whether or not they were planning to vote for the incumbent president for re-election, and no other choices were possible. 739 of them replied that they were planning on not voting for the incumbent president for re-election. The president claims that more than half of all voters will vote for him.

A. Verify that the P-Value for the proportion of voters that will vote for the incumbent president is 28%

B. Can we conclude that more than half of voters are planning on voting for the incumbent president? Explain.

Answer 1

H0: p = 0.50

Ha: p > 0.50

Sample proportion = 739 / 1500 = 0.4927

Test statistics

z = ( - p) / sqrt [ p( 1 - p) / n]

= (0.4927 - 0.50) / sqrt ( 0.50 * 0.50 / 1500)

= -0.57

P-value = P(Z < z)

= P(Z < -0.57)

= 0.2843

That is p-value = 28%

b)

Since p-value > 0.05 significance level, we do not have sufficient evidence to support the claim that more

than half of voters are planning on voting for the incumbent president.