A sociologist found that in a random sample of 50 retired men, the average number of jobs they had during their lifetime was 7.2. The population standard deviation is 2.1. Assume the population is normally distributed. Find the 99% confidence interval of the mean number of jobs. The text provided is from an educational exercise focusing on statistics and confidence intervals. It involves finding the confidence interval for a population mean ($\mu$).### Step-by-Step Breakdown:1. **Problem Statement Options:** - The population standard deviation is given. - The exercise does not require finding the sample size. - The exercise asks to estimate the confidence interval of the population mean.2. **Instructions:** - Round calculated values to two decimal places.3. **Confidence Interval Input:** - Two input boxes are provided to input the lower and upper bounds of the confidence interval. The true mean ($\mu$) is expected to fall within this range.4. **Confidence Level:** - The confidence level is set at 99%. This means there is a 99% certainty that the true mean number of jobs a person has during their lifetime lies within the specified range.5. **Feedback Options:** - A link is provided to message the instructor for help with the question.6. **Action:** - A blue "Submit Question" button is available for submitting answers.This setup aids learners in understanding how to calculate and interpret confidence intervals in the context of statistical analysis.

Solution: Let X be the random variable defined as the number of jobs a man had during his lifetime…

Answered: A sociologist found that in a random…

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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A sociologist found that in a random sample of 50 retired men, the average number of jobs they had during their lifetime was 7.2. The population standard deviation is 2.1. Assume the population is normally distributed. Find the 99% confidence interval of the mean number of jobs.

The text provided is from an educational exercise focusing on statistics and confidence intervals. It involves finding the confidence interval for a population mean ($\mu$).

### Step-by-Step Breakdown:

1. **Problem Statement Options:**
- The population standard deviation is given.
- The exercise does not require finding the sample size.
- The exercise asks to estimate the confidence interval of the population mean.

2. **Instructions:**
- Round calculated values to two decimal places.

3. **Confidence Interval Input:**
- Two input boxes are provided to input the lower and upper bounds of the confidence interval. The true mean ($\mu$) is expected to fall within this range.

4. **Confidence Level:**
- The confidence level is set at 99%. This means there is a 99% certainty that the true mean number of jobs a person has during their lifetime lies within the specified range.

5. **Feedback Options:**
- A link is provided to message the instructor for help with the question.

6. **Action:**
- A blue "Submit Question" button is available for submitting answers.

This setup aids learners in understanding how to calculate and interpret confidence intervals in the context of statistical analysis.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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