Question

Q6. You are the assistant director of political research for the NBC television network, and two candidates Jeffrey Temple and Rotenberg Marvel, are running for president of the United States. You need to furnish a prediction of the percentage of the vote going to Marin, assuming the election was held today, for tomorrow’s evening newscast. You want to be 93% confident in your prediction and desire a total precision of ±4 percentage points.

a) Assume that you have no reliable information concerning the percentage of the population that prefers Marvel. What sample size will you use for the project? Hint: in this case, you should be conservative assuming the maximum degree of heterogeneity in the population so as to have a sample that is larger than it is necessary.

b) Assume that a similar poll, taken thirty days ago, revealed that 43 percent of the respondents would vote for Marvel. Taking this information into account, what sample size will you use for the project?

Answer 1

Solution :

Given that,

= 1 - = 0.5

margin of error = E = 0.04

At 93% confidence level

= 1 - 93%

=1 - 0.93 =0.07

/2 = 0.035

Z/2 = 1.812

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (1.812 / 0.04)² * 0.5 * 0.5

= 513.02

sample size = n = 514

b) = 0.43

1 - = 1 - 0.43 = 0.57

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (1.812 / 0.04)² * 0.43 * 0.57

= 502.96

sample size = n = 503