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.
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.
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ISBN:9781119256830
Author:Amos Gilat
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![**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:
\[
\text{Margin of Error} = z \times \sqrt{\frac{\hat{p} \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02ea3ac7-5fea-4059-9e9c-bdba4fa24b5b%2F4aade04a-0369-44f1-983f-4fda0808f8b5%2Fuub2bz.png&w=3840&q=75)
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} \
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