**Statistical Decision-Making in Passenger Preferences**In this activity, you will play the role of an operations manager for an airline. Your task is to determine the number of passengers to survey to make data-driven decisions about offering higher fare levels for aisle seats. Specifically, you need to ensure that the sample percentage is within 4.5 percentage points of the true population percentage with a 95% confidence level.### Instructions1. **Understanding the Scenario:** - How many randomly selected air passengers must you survey? - You aim to achieve a 95% confidence level that the sample percentage will be within 4.5 percentage points of the true population percentage.2. **Tasks:** a. **No Prior Knowledge:** - Assume that nothing is known about the percentage of passengers who prefer aisle seats. - Determine the sample size (n). Formula for sample size when no prior proportion is known (p = 0.5): \[ n = \left( \frac{Z^2 \times p \times (1 - p)}{E^2} \right) \] where $ Z $ is the z-score for 95% confidence (1.96), $ p $ is the assumed proportion (0.5), and $ E $ is the margin of error (0.045). `n = [Enter your answer here]` *(Round up to the nearest integer.)* b. **Using Prior Survey Data:** - Assume that a prior survey suggests that about 35% of air passengers prefer an aisle seat. - Determine the sample size (n). Formula for sample size when prior proportion is known: \[ n = \left( \frac{Z^2 \times p \times (1 - p)}{E^2} \right) \] where $ Z $ is the z-score for 95% confidence (1.96), $ p $ is the estimated proportion (0.35), and $ E $ is the margin of error (0.045). `n = [Enter your answer here]` *(Round up to the nearest integer.)*### NoteRemember to round both sample size values to the nearest integer for practical purposes.### Enter Your Answers- Enter your calculated sample sizes in each of the provided answer boxes.This

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 confident that the sample percentage is within 4.5 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. (Round up to the nearest integer.) b. Assume that a prior survey suggests that about 35% of air passengers prefer an aisle seat. (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 confident that the sample percentage is within 4.5 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. (Round up to the nearest integer.) b. Assume that a prior survey suggests that about 35% of air passengers prefer an aisle seat. (Round up to the nearest integer.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

**Statistical Decision-Making in Passenger Preferences**

In this activity, you will play the role of an operations manager for an airline. Your task is to determine the number of passengers to survey to make data-driven decisions about offering higher fare levels for aisle seats. Specifically, you need to ensure that the sample percentage is within 4.5 percentage points of the true population percentage with a 95% confidence level.

### Instructions

1. **Understanding the Scenario:**
- How many randomly selected air passengers must you survey?
- You aim to achieve a 95% confidence level that the sample percentage will be within 4.5 percentage points of the true population percentage.

2. **Tasks:**

a. **No Prior Knowledge:**
- Assume that nothing is known about the percentage of passengers who prefer aisle seats.
- Determine the sample size (n).

Formula for sample size when no prior proportion is known (p = 0.5):
\[
n = \left( \frac{Z^2 \times p \times (1 - p)}{E^2} \right)
\]
where $ Z $ is the z-score for 95% confidence (1.96), $ p $ is the assumed proportion (0.5), and $ E $ is the margin of error (0.045).

`n = [Enter your answer here]`

*(Round up to the nearest integer.)*

b. **Using Prior Survey Data:**
- Assume that a prior survey suggests that about 35% of air passengers prefer an aisle seat.
- Determine the sample size (n).

Formula for sample size when prior proportion is known:
\[
n = \left( \frac{Z^2 \times p \times (1 - p)}{E^2} \right)
\]
where $ Z $ is the z-score for 95% confidence (1.96), $ p $ is the estimated proportion (0.35), and $ E $ is the margin of error (0.045).

`n = [Enter your answer here]`

*(Round up to the nearest integer.)*

### Note
Remember to round both sample size values to the nearest integer for practical purposes.

### Enter Your Answers
- Enter your calculated sample sizes in each of the provided answer boxes.

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