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 u. Use the accompanying data on absences for days to obtain a 95% large-sample CI for u. Number of absences 0 1 2 3 4567 89 10 Frequency 147 11 9 6 6 221 1 [Hint: The mean and variance of a Poisson variable both equal u, so X- u VH/n 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 u.] (Round your answers two decimal places.

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 u. Use the accompanying data on absences for days to obtain a 95% large-sample CI for u. Number of absences 0 1 2 3 4567 89 10 Frequency 147 11 9 6 6 221 1 [Hint: The mean and variance of a Poisson variable both equal u, so X- u VH/n 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 u.] (Round your answers two decimal places.

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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Concept explainers

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

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 $ \mu $. Use the accompanying data on absences for 50 days to obtain a 95% large-sample confidence interval for $ \mu $.

| Number of absences | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|--------------------|---|---|---|---|---|---|---|---|---|---|----|
| Frequency | 1 | 4 | 7 | 11| 9 | 6 | 6 | 2 | 2 | 1 | 1 |

*[Hint: The mean and variance of a Poisson variable both equal $ \mu $, so]*

\[
Z = \frac{\bar{X} - \mu}{\sqrt{\mu/n}}
\]

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 - \alpha $) and solving the resulting inequalities for $ \mu $. *(Round your answers to two decimal places.)*

\[ \left( \boxed{\phantom{XXX}}, \boxed{\phantom{XXX}} \right) \]

**Explanation of the Data:**

- The table shows the frequency of teacher absences over 50 days.
- The number of absences ranges from 0 to 10.
- Each number of absences has a corresponding frequency indicating how many days that number of absences occurred.

**Statistical Note:**

- The approach uses a Poisson distribution where both the mean and variance are equal to $ \mu $.
- The standard normal distribution is used to derive the confidence interval.

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