Question

A survey of 650 people reported that 32% favored the reelection of the current mayor. Which of the following correctly interprets the margin of error for a 90% confidence interval?(1 point)
Responses

With 99% confidence, the sample proportion of people who favor the reelection of the current mayor falls between (0.29,0.35)
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With 99% confidence, the sample proportion of people who favor the reelection of the current mayor falls between left parenthesis 0.29 comma 0.35 right parenthesis .

With 90% confidence, the sample proportion of people who favor the reelection of the current mayor falls between (0.32,0.36)
.
With 90% confidence, the sample proportion of people who favor the reelection of the current mayor falls between left parenthesis 0.32 comma 0.36 right parenthesis .

With 90% confidence, the sample proportion of people who favor the reelection of the current mayor falls between (0.29,0.35)
.
With 90% confidence, the sample proportion of people who favor the reelection of the current mayor falls between left parenthesis 0.29 comma 0.35 right parenthesis .

With 90% confidence, the sample proportion of people who favor the reelection of the current mayor falls between (0.58,0.64)
.
With 90% confidence, the sample proportion of people who favor the reelection of the current mayor falls between left parenthesis 0.58 comma 0.64 right parenthesis .

Answer 1

The correct choice is: With 90% confidence, the proportion falls between (0.29, 0.35).

Reason: p̂ = 0.32, SE = sqrt(0.32·0.68/650) ≈ 0.0183, z* = 1.645 for 90% → ME = 1.645·0.0183 ≈ 0.030. So the 90% CI ≈ 0.32 ± 0.03 = (0.29, 0.35).

(Technical note: the interval actually refers to the population proportion, not the sample proportion.)