Question

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.

Answer 1

Answer with explanation:

As per given , we have

p= 0.457

n= 1033

Margin of error for 99​% confidence : E= 4%=0.04

Confidence interval : $p\pm E$

i.e. $0.457\pm 0.04$

$=( 0.457- 0.04,\ 0.457+0.04)=(0.417,\ 0.497)$

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).