QuestionJuly 19, 2025

You are the operations manager for an airline and you are considering a higher fare level for passengers in aisle seats . How many randomly selected air passengers must you survey? Assume that you want to be 90% confident that the sample percentage is within 3.55 percentage points of the true population percentage Complete parts (a) and (b) below. a. Assume that nothing is known about the percentage of passengers who prefer aisle seats. n=555 (Round up to the nearest integer.) b. Assume that a prior survey suggests that about 37% of air passengers prefer an aisle seat. n=square (Round up to the nearest integer.)

You are the operations manager for an airline and you are considering a higher fare level for passengers in aisle seats . How many randomly selected air passengers must you survey? Assume that you want to be 90% confident that the sample percentage is within 3.55 percentage points of the true population percentage Complete parts (a) and (b) below. a. Assume that nothing is known about the percentage of passengers who prefer aisle seats. n=555 (Round up to the nearest integer.) b. Assume that a prior survey suggests that about 37% of air passengers prefer an aisle seat. n=square (Round up to the nearest integer.)
You are the operations manager for an airline and you are considering a higher fare level for
passengers in aisle seats . How many randomly selected air passengers must you survey? Assume
that you want to be 90%  confident that the sample percentage is within 3.55 percentage points of the
true population percentage Complete parts (a) and (b) below.
a. Assume that nothing is known about the percentage of passengers who prefer aisle seats.
n=555
(Round up to the nearest integer.)
b. Assume that a prior survey suggests that about 37%  of air passengers prefer an aisle seat.
n=square 
(Round up to the nearest integer.)

Solution
4.2(167 votes)

Answer

n = 485 Explanation 1. Determine the formula for sample size Use the formula for sample size estimation: n = \left(\frac{Z^2 \cdot p \cdot (1-p)}{E^2}\right), where Z is the z-score for confidence level, p is the estimated proportion, and E is the margin of error. 2. Calculate sample size with unknown proportion For part (a), assume p = 0.5 (worst-case scenario). The z-score for 90\% confidence is 1.645. Margin of error E = 0.035. Substitute into the formula: n = \left(\frac{1.645^2 \cdot 0.5 \cdot 0.5}{0.035^2}\right) = 554.57. Round up to nearest integer: n = 555. 3. Calculate sample size with known proportion For part (b), use p = 0.37. Substitute into the formula: n = \left(\frac{1.645^2 \cdot 0.37 \cdot 0.63}{0.035^2}\right) = 484.47. Round up to nearest integer: n = 485.

Explanation

1. Determine the formula for sample size<br /> Use the formula for sample size estimation: $n = \left(\frac{Z^2 \cdot p \cdot (1-p)}{E^2}\right)$, where $Z$ is the z-score for confidence level, $p$ is the estimated proportion, and $E$ is the margin of error.<br /><br />2. Calculate sample size with unknown proportion<br /> For part (a), assume $p = 0.5$ (worst-case scenario). The z-score for $90\%$ confidence is $1.645$. Margin of error $E = 0.035$. Substitute into the formula: $n = \left(\frac{1.645^2 \cdot 0.5 \cdot 0.5}{0.035^2}\right) = 554.57$. Round up to nearest integer: $n = 555$.<br /><br />3. Calculate sample size with known proportion<br /> For part (b), use $p = 0.37$. Substitute into the formula: $n = \left(\frac{1.645^2 \cdot 0.37 \cdot 0.63}{0.035^2}\right) = 484.47$. Round up to nearest integer: $n = 485$.
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