help ### Statistical Analysis of Unemployment Duration**Problem Statement:**A leading magazine reported at one time that the average number of weeks an individual is unemployed is 29 weeks. Assume that for the population of all unemployed individuals, the population mean length of unemployment is 29 weeks and that the population standard deviation is 3.5 weeks. Suppose you would like to select a random sample of 77 unemployed individuals for a follow-up study.**Objective:**Find the probability that a sample of size $ n = 77 $ is randomly selected with a mean greater than 29.9. You can use Statcrunch to answer this question.---This problem focuses on the application of statistical methods to determine the probability of a particular sample mean, given the parameters of the population. Here is a step-by-step guide to approaching this problem:1. **Identify Key Parameters:** - Population Mean ($ \mu $): 29 weeks - Population Standard Deviation ($ \sigma $): 3.5 weeks - Sample Size ($ n $): 772. **Calculate the Standard Error of the Mean (SEM):** \[ SEM = \frac{\sigma}{\sqrt{n}} = \frac{3.5}{\sqrt{77}} \]3. **Determine the Z-Score for the Sample Mean:** The Z-Score represents the number of standard deviations that a sample mean is from the population mean. \[ Z = \frac{(X - \mu)}{SEM} \] where $ X $ is the sample mean (29.9 weeks in this case).4. **Use the Z-Score to Find the Probability:** - Look up the Z-Score in the standard normal distribution table or use a software tool like Statcrunch to find the corresponding probability. 5. **Interpret the Results:** The final step involves interpreting the probability value. A higher probability indicates that a sample mean greater than 29.9 weeks is not very unusual, while a lower probability implies that such a sample mean is relatively rare.By following these steps, you will be able to determine the likelihood of selecting a sample with a mean unemployment duration greater than 29.9 weeks from the population. This kind of analysis is useful for making inferences about population parameters based on sample data.

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Description: help ### Statistical Analysis of Unemployment Duration**Problem Statement:**A leading magazine reported at one time that the average number of weeks an individual is unemployed is 29 weeks. Assume that for the population of all unemployed individuals

We have given that X~N(mu,sigma ^2) mu=29 ,sigma =3.5 Z-socre =(x-mu)/sigma

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A leading magazine reported at one time that the average number of weeks an individual is unemployed is 29 weeks. Assume that for the population unemployed individuals the population mean length of unemployment is 29 weeks and that the population standard deviation is 3.5 weeks. Suppose you would like to select a random sample of 77 unemployed individuals for a follow- up study. Find the probability that a sample of size n=77 is randomly selected with a mean greater than 29.9. You can use Statcrunch to answer this question. all

A leading magazine reported at one time that the average number of weeks an individual is unemployed is 29 weeks. Assume that for the population unemployed individuals the population mean length of unemployment is 29 weeks and that the population standard deviation is 3.5 weeks. Suppose you would like to select a random sample of 77 unemployed individuals for a follow- up study. Find the probability that a sample of size n=77 is randomly selected with a mean greater than 29.9. You can use Statcrunch to answer this question. all

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Problem 1P

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help

### Statistical Analysis of Unemployment Duration

**Problem Statement:**
A leading magazine reported at one time that the average number of weeks an individual is unemployed is 29 weeks. Assume that for the population of all unemployed individuals, the population mean length of unemployment is 29 weeks and that the population standard deviation is 3.5 weeks. Suppose you would like to select a random sample of 77 unemployed individuals for a follow-up study.

**Objective:**
Find the probability that a sample of size $ n = 77 $ is randomly selected with a mean greater than 29.9. You can use Statcrunch to answer this question.

---

This problem focuses on the application of statistical methods to determine the probability of a particular sample mean, given the parameters of the population. Here is a step-by-step guide to approaching this problem:

1. **Identify Key Parameters:**
- Population Mean ($ \mu $): 29 weeks
- Population Standard Deviation ($ \sigma $): 3.5 weeks
- Sample Size ($ n $): 77

2. **Calculate the Standard Error of the Mean (SEM):**
\[
SEM = \frac{\sigma}{\sqrt{n}} = \frac{3.5}{\sqrt{77}}
\]

3. **Determine the Z-Score for the Sample Mean:**
The Z-Score represents the number of standard deviations that a sample mean is from the population mean.
\[
Z = \frac{(X - \mu)}{SEM}
\]
where $ X $ is the sample mean (29.9 weeks in this case).

4. **Use the Z-Score to Find the Probability:**
- Look up the Z-Score in the standard normal distribution table or use a software tool like Statcrunch to find the corresponding probability.

5. **Interpret the Results:**
The final step involves interpreting the probability value. A higher probability indicates that a sample mean greater than 29.9 weeks is not very unusual, while a lower probability implies that such a sample mean is relatively rare.

By following these steps, you will be able to determine the likelihood of selecting a sample with a mean unemployment duration greater than 29.9 weeks from the population. This kind of analysis is useful for making inferences about population parameters based on sample data.

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