Questions: 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 2.5 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=1083 (Round up to the nearest integer.) b. Assume that a prior survey suggests that about 36% of air passengers prefer an aisle seat. n= (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 2.5 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=1083

(Round up to the nearest integer.)

b. Assume that a prior survey suggests that about 36% of air passengers prefer an aisle seat.

n=

(Round up to the nearest integer.)

Transcript text: 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 2.5 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. \[ n=1083 \] (Round up to the nearest integer.) b. Assume that a prior survey suggests that about $36 \%$ of air passengers prefer an aisle seat. \[ \mathrm{n}=\square \] (Round up to the nearest integer.)

Solution

Solution Steps

Step 1: Identify the Parameters

The desired confidence level corresponds to a Z-score of 1.645. The margin of error (E) is set at 0.025. The population proportion (p) is estimated to be 0.36. We aim to round the answer to 2 decimal places, but for sample size, we round up to the nearest whole number.

Step 2: Apply the Sample Size Formula

The formula to calculate the minimum sample size $n$ is: \[n = \left( \frac{Z^2 \cdot p \cdot (1 - p)}{E^2} \right)\] Substituting the values, we get $n = \left( \frac{1.645^2 \cdot 0.36 \cdot (1 - 0.36)}{0.025^2} \right)$.

Step 3: Calculation

After calculation, the initial sample size is 997.55. Rounding up, the minimum required sample size $n$ is 998.