Q:

Suppose a polling agency reported that 45.7% of registered voters were in favor of raising income taxes to pay down the national debt. The agency states that results are based on telephone interviews with a random sample of 1033 registered voters. Suppose the agency states the margin of error for 99​% confidence is 4.0​%. Determine and interpret the confidence interval for the proportion of registered voters who are in favor of raising income taxes to pay down the national debt.

Accepted Solution

A:
Answer with explanation:As per given , we havep= 0.457n= 1033Margin of error for 99​% confidence : E= 4%=0.04Confidence interval : [tex]p\pm E[/tex]i.e. [tex] 0.457\pm 0.04[/tex] [tex]=( 0.457- 0.04,\ 0.457+0.04)=(0.417,\ 0.497) [/tex]99% confidence interval for the proportion of registered voters who are in favor of raising income taxes to pay down the national debt. = (0.417, 0.497)Interpretation : We are 99% sure that the true population proportion of registered voters who are in favor of raising income taxes to pay down the national debt lies in interval (0.417, 0.497).