You may need to use the appropriate appendix table or technology to answer this question.Older people often have a hard time finding work. A research group reported on the number of weeks it takes a worker aged 55 plus to find a job. The data on number of weeks spent searching for a job is given in the table below.(a) Provide a point estimate of the population mean number of weeks it takes a worker aged 55 plus to find a job.———Weeks(b) At 95% confidence, what is the margin of error? (Round your answer to four decimal places.)———Weeks (c) What is the 95% confidence interval estimate of the mean? (Round your answers to two decimal places.)————-Weeks to ————- weeks. ### Job Search Duration Analysis#### Research DataA study was conducted to analyze the time people often spend searching for a job. The findings are summarized in the following table, which lists the number of weeks individuals reported spending in their job search:| 21 | 14 | 51 | 16 | 17 | 14 | 16 | 12 | 48 | 0 ||----|----|----|----|----|----|----|----|----|----|| 27 | 17 | 32 | 24 | 12 | 10 | 52 | 21 | 26 | 14 || 13 | 24 | 19 | 28 | 26 | 10 | 21 | 44 | 36 | || 22 | 39 | 17 | 17 | 10 | 19 | 16 | 22 | 5 | 22 |#### Statistical Analysis**Point Estimate Calculation:**To understand the central tendency of the job search duration, we calculate the point estimate of the population mean number of weeks it takes for an individual to find a job. Based on the data provided, the point estimate is determined as:\[ \text{Point Estimate} = 22 \, \text{weeks} \]**Margin of Error:**To provide a range within which the true population mean likely falls, we calculate the margin of error at a 95% confidence level. The margin of error for this data is:\[ \text{Margin of Error} = \pm 3.802 \, \text{weeks} \]This analysis indicates that, on average, individuals spend approximately 22 weeks searching for a job, with a possible variation of 3.802 weeks in either direction to account for sampling variability.

The question is about confidence intervalGiven :To find :a ) Pt. estimate of the popl. mean no. of…

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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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You may need to use the appropriate appendix table or technology to answer this question. Older people often have a hard time finding work. A research group reported on the number of weeks it takes a worker aged 55 plus to find a job. The data on number of weeks spent searching for a job is given in the table below. (a) Provide a point estimate of the population mean number of weeks it takes a worker aged 55 plus to find a job. ———Weeks (b) At 95% confidence, what is the margin of error? (Round your answer to four decimal places.) ———Weeks (c) What is the 95% confidence interval estimate of the mean? (Round your answers to two decimal places.) ————-Weeks to ————- weeks.

### Job Search Duration Analysis

#### Research Data
A study was conducted to analyze the time people often spend searching for a job. The findings are summarized in the following table, which lists the number of weeks individuals reported spending in their job search:

| 21 | 14 | 51 | 16 | 17 | 14 | 16 | 12 | 48 | 0 |
|----|----|----|----|----|----|----|----|----|----|
| 27 | 17 | 32 | 24 | 12 | 10 | 52 | 21 | 26 | 14 |
| 13 | 24 | 19 | 28 | 26 | 10 | 21 | 44 | 36 | |
| 22 | 39 | 17 | 17 | 10 | 19 | 16 | 22 | 5 | 22 |

#### Statistical Analysis
**Point Estimate Calculation:**
To understand the central tendency of the job search duration, we calculate the point estimate of the population mean number of weeks it takes for an individual to find a job. Based on the data provided, the point estimate is determined as:
\[ \text{Point Estimate} = 22 \, \text{weeks} \]

**Margin of Error:**
To provide a range within which the true population mean likely falls, we calculate the margin of error at a 95% confidence level. The margin of error for this data is:
\[ \text{Margin of Error} = \pm 3.802 \, \text{weeks} \]

This analysis indicates that, on average, individuals spend approximately 22 weeks searching for a job, with a possible variation of 3.802 weeks in either direction to account for sampling variability.

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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