Air Connect airlines found that 97 out of a random sample of 169 passengers purchased round-trip tickets. Let p be the proportion of all Air Connect passengers who purchase round trip tickets. Find a 95 percent confidence interval for p.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
Practice Pack

I need help finding the answers that go into the yellow highlighted boxes :) Thank you so much!!

**Air Connect Airlines: Confidence Interval for Round-Trip Ticket Purchase**

Air Connect Airlines found that 97 out of a random sample of 169 passengers purchased round-trip tickets. Let \( p \) be the proportion of all Air Connect passengers who purchase round-trip tickets. Find a 95 percent confidence interval for \( p \).

| Parameter                    | Description                                       | Instructions                                |
|------------------------------|---------------------------------------------------|---------------------------------------------|
| \( n \)                      | Number of passengers sampled                      |                                             |
| \( x \)                      | Number of passengers who purchased round-trip tickets |                                             |
| \( \hat{p} \)                | Sample proportion ( \( \hat{p} = \frac{x}{n} \) ) | Round off to 3 decimal places               |
| \( \hat{q} = 1 - \hat{p} \)  | Complement of sample proportion                   |                                             |
| Confidence Level             | Desired confidence level                         |                                             |
| \( z \) value                | Z-score associated with confidence level          | Round off to 2 decimal places               |
| Margin of Error              | Calculated margin of error                       | \( \text{M. of E.} = z \times \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \) |
|                              |                                                   |                                             |
| Point Estimate               | The sample proportion \( \hat{p} \)              |                                             |
| Lower Limit                  | Lower limit of the confidence interval            | Round off to 3 decimal places               |
| Upper Limit                  | Upper limit of the confidence interval            | Round off to 3 decimal places               |
|                              |                                                   |                                             |
| Interpret the confidence interval in context of the problem | Provide interpretation of results            |                                             |

**Steps to Calculate:**

1. Compute the sample proportion \( \hat{p} \):
   \[
   \hat{p} = \frac{x}{n}
   \]
   
2. Calculate the complement of the sample proportion:
   \[
   q = 1 - \hat{p}
   \]

3. Determine the z-value for the given confidence level (for a 95% confidence level, the z-value is approximately 1.96).

4. Compute the margin of error:
   \[
   \text{Margin of Error} = z \times \sqrt{\frac{\hat{p} \
Transcribed Image Text:**Air Connect Airlines: Confidence Interval for Round-Trip Ticket Purchase** Air Connect Airlines found that 97 out of a random sample of 169 passengers purchased round-trip tickets. Let \( p \) be the proportion of all Air Connect passengers who purchase round-trip tickets. Find a 95 percent confidence interval for \( p \). | Parameter | Description | Instructions | |------------------------------|---------------------------------------------------|---------------------------------------------| | \( n \) | Number of passengers sampled | | | \( x \) | Number of passengers who purchased round-trip tickets | | | \( \hat{p} \) | Sample proportion ( \( \hat{p} = \frac{x}{n} \) ) | Round off to 3 decimal places | | \( \hat{q} = 1 - \hat{p} \) | Complement of sample proportion | | | Confidence Level | Desired confidence level | | | \( z \) value | Z-score associated with confidence level | Round off to 2 decimal places | | Margin of Error | Calculated margin of error | \( \text{M. of E.} = z \times \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \) | | | | | | Point Estimate | The sample proportion \( \hat{p} \) | | | Lower Limit | Lower limit of the confidence interval | Round off to 3 decimal places | | Upper Limit | Upper limit of the confidence interval | Round off to 3 decimal places | | | | | | Interpret the confidence interval in context of the problem | Provide interpretation of results | | **Steps to Calculate:** 1. Compute the sample proportion \( \hat{p} \): \[ \hat{p} = \frac{x}{n} \] 2. Calculate the complement of the sample proportion: \[ q = 1 - \hat{p} \] 3. Determine the z-value for the given confidence level (for a 95% confidence level, the z-value is approximately 1.96). 4. Compute the margin of error: \[ \text{Margin of Error} = z \times \sqrt{\frac{\hat{p} \
Expert Solution
trending now

Trending now

This is a popular solution!

video

Learn your way

Includes step-by-step video

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Knowledge Booster
Propositional Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman