Question

A poll of 3,200 voters were asked what they thought the most significant issue was in the upcoming election. Sixty-eight percent answered the economy.

a) Construct a 90% confidence interval for the population proportion of voters who feel the economy is the most important issue. Write a complete sentence describing the meaning of this confidence interval.

b) Construct a 95% confidence interval for the population proportion of voters who feel the economy is the most important issue. Write a complete sentence describing the meaning of this confidence interval.

c) Explain, using complete sentences, why the confidence interval in part b) is wider.

Answer 1

a. z value for 90% CI is 1.645 as P(-1.645<z<1.645)=0.90

So Margin of Error is

Hence CI is

b. z value for 95% CI is 1.96 as P(-1.96<z<1.96)=0.95

So Margin of Error is

Hence CI is

c. As we increased the confidence level, z value increases and so the Margin of Error increases given wider CI.