The superintendent of a large school district, having once had a course in probability and statistics, believes that the number of teachers absent on any given day has a Poisson distribution with parameter μ. Use the accompanying data on absences for 50 days to obtain a 95% large-sample CI for μ. Number of absences 012 3 4 5 6 7 8 9 10 Frequency 1 3 8 10 9 7 5 4 1 1 1 [Hint: The mean and variance of a Poisson variable both equal μ, so X-μ Vμ/n Z=== has approximately a standard normal distribution. Now proceed as in the derivation of the interval for p by making a probability statement (with probability 1-a) and solving the resulting inequalities for μ.] (Round your answers to two decimal places.) 3.53 1x 4.66 x
The superintendent of a large school district, having once had a course in probability and statistics, believes that the number of teachers absent on any given day has a Poisson distribution with parameter μ. Use the accompanying data on absences for 50 days to obtain a 95% large-sample CI for μ. Number of absences 012 3 4 5 6 7 8 9 10 Frequency 1 3 8 10 9 7 5 4 1 1 1 [Hint: The mean and variance of a Poisson variable both equal μ, so X-μ Vμ/n Z=== has approximately a standard normal distribution. Now proceed as in the derivation of the interval for p by making a probability statement (with probability 1-a) and solving the resulting inequalities for μ.] (Round your answers to two decimal places.) 3.53 1x 4.66 x
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Data Analysis Using Poisson Distribution for Teacher Absences**
The superintendent of a large school district, with a background in probability and statistics, believes that the number of teachers absent on any given day follows a Poisson distribution with parameter \( \mu \). The goal is to use the provided data on absences over 50 days to determine a 95% large-sample confidence interval (CI) for \( \mu \).
**Data Table: Absences**
| Number of Absences | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|--------------------|---|---|---|---|---|---|---|---|---|---|----|
| Frequency | 1 | 3 | 8 | 10| 9 | 7 | 5 | 4 | 1 | 1 | 1 |
*Hint:* The mean and variance of a Poisson variable both equal \( \mu \), so
\[
Z = \frac{\bar{X} - \mu}{\sqrt{\mu / n}}
\]
approximates a standard normal distribution. Proceed by deriving the interval for \( p \) by creating a probability statement (with probability \( 1 - \alpha \)) and solving the resulting inequalities for \( \mu \). Round your answers to two decimal places.
**Answer:** \( (3.53, 4.66) \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F62b236b3-1e1c-48f8-a6f5-9c3f49a681da%2F1500156b-f9de-4c40-9bad-6ae18e370e68%2F0ljeif_processed.png&w=3840&q=75)
Transcribed Image Text:**Data Analysis Using Poisson Distribution for Teacher Absences**
The superintendent of a large school district, with a background in probability and statistics, believes that the number of teachers absent on any given day follows a Poisson distribution with parameter \( \mu \). The goal is to use the provided data on absences over 50 days to determine a 95% large-sample confidence interval (CI) for \( \mu \).
**Data Table: Absences**
| Number of Absences | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|--------------------|---|---|---|---|---|---|---|---|---|---|----|
| Frequency | 1 | 3 | 8 | 10| 9 | 7 | 5 | 4 | 1 | 1 | 1 |
*Hint:* The mean and variance of a Poisson variable both equal \( \mu \), so
\[
Z = \frac{\bar{X} - \mu}{\sqrt{\mu / n}}
\]
approximates a standard normal distribution. Proceed by deriving the interval for \( p \) by creating a probability statement (with probability \( 1 - \alpha \)) and solving the resulting inequalities for \( \mu \). Round your answers to two decimal places.
**Answer:** \( (3.53, 4.66) \)
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