Question

Political parties rely heavily upon polling to measure their support in the electorate. In a country with four major political parties, a poll is conducted and the Coffee Party is supported by 435 of the 1183 randomly-selected voters who were polled.

A) The Coffee Party leader claim that they have the support of 42% of the electorate. Construct and interpret a 98% confidence interval to estimate the proportion of voters who support the Coffee Party in the country and indicate whether or not your interval suggests that this claim is plausible? Explain.
B) Suppose the random smple was actually 1200 people, but 17 people never responded. What type of bias is the and how could this potentially change your conclusion to part (a)? Explain.

Answer 1

a) The claim is not plausible

b) claim is plausible and the type of bias here is response bias

Explanation:

Given data:

Number of political parties = 4

coffee party got the support of 435 out of 1183 randomly selected voters in a poll conducted.

A) Construct and interpret a 98% confidence interval to estimate the proportion of voters who support the coffee party

H0 ( null hypothesis ) : p = 0.42

Ha ( alternate hypothesis ) : p ≠ 0.42

z value for 98% confidence interval = 2.326

using 98% confidence interval the value of p = ( 0.3668, 0.3686 )

hence the claim is not plausible

B) Determine the type of bias

Assume the actual number of people = 1200

and 17 people did not respond

hence number of people who responded = 1200 - 17 = 1183

Therefore the claim by the manager is plausible because 17 people did not respond and the type of bias here is response bias

attached below is a detailed solution of the problem of the A part