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 445 of the 11834 randomly selected registered voters who were polled.

(a) The Coffee Party leader claim that they have the support of 42% of the electorate. Construct and interpret a 99% confidence interval to estimate the proportion of registered voters who support the Coffee Party in the country and indicate whether or not your interval suggests that this claim is plausible? Explain your reason.

(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

Solution(A)

Ho:p=0.42

Ha:p not = 0.42

z crit for 99%=2.576

sample proportion of voters supported Coffee Party =p^=x/n=445/11834= 0.03760352

99% confidence interval for p is

p^-z*sqrt(p^*(1-p^)/n,p^+z*sqrt(p^*(1-p^)/n

0.03760352-2.576*sqrt(0.03760352*(1-0.03760352)/11834),0.03760352+2.576*sqrt(0.03760352*(1-0.03760352)/11834)

0.03309876, 0.04210828

since it does not contain 0.42

Reject Ho

at 99% level of significance ,claim is not plausible

Solution-B:

n=1200

people responded=1200-17= 1183

1183 responded may support coffee party or not

Type of bias is response bias

This results in claim is plausible that The Coffee Party leader claim that they have the support of 42% of the electorate.