From the estimation of the population mean of the Year of Education with a 99% confidence interval, what is the lower limit? (Round off to two decimal places if necessary). **Table 1. Data from Random Sampling**The table below presents data collected from a random sample. The columns represent different categories, and the rows provide specific data points for each individual in the sample.| Monthly Income ($1,000) | Marital Status | Year of Education | Type of Punishment | Sentence Year ||------------------------|----------------|-------------------|--------------------|--------------|| 1.8 | 2 | 8 | 2 | 8 || 2.3 | 3 | 7 | 1 | 9 || 2.5 | 1 | 10 | 2 | 18 || 2.3 | 1 | 9 | 1 | 22 || 1.9 | 2 | 14 | 1 | 8 || 1.9 | 1 | 11 | 1 | 15 || 1.9 | 2 | 14 | 2 | 20 || 2.1 | 3 | 12 | 1 | 6 || 1.9 | 2 | 7 | 1 | 15 || 2.1 | 2 | 10 | 3 | 9 || 2.1 | 3 | 12 | 2 | 19 || 2.0 | 1 | 8 | 2 | 14 || 2.6 | 2 | 8 | 2 | 13 || 2.6 | 1 | 9 | 1 | 9 || 2.0 | 1 | 7 | 2 | 11 || 2.6 | 1 | 12 | 3 | 7 || 1.9 | 2 | 9 | 1 | 11 || 2.5 | 3 | 7 | 2 | 7 || 2.1 ### Types of Punishment1. **Probation/Community Service**2. **Jail Incarceration**3. **Prison Incarceration**### Marital Status1. **Married**2. **Single**3. **Other**This chart is a classification system for types of punishment and marital status, using numerical identifiers for each category. It is organized into two sections: "Type of Punishment" and "Marital Status," each listing options with corresponding numbers for easy reference in data analysis or educational purposes.

Answered: From the estimation of the population…

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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Question

From the estimation of the population mean of the Year of Education with a 99% confidence interval, what is the lower limit? (Round off to two decimal places if necessary).

**Table 1. Data from Random Sampling**

The table below presents data collected from a random sample. The columns represent different categories, and the rows provide specific data points for each individual in the sample.

| Monthly Income ($1,000) | Marital Status | Year of Education | Type of Punishment | Sentence Year |
|------------------------|----------------|-------------------|--------------------|--------------|
| 1.8 | 2 | 8 | 2 | 8 |
| 2.3 | 3 | 7 | 1 | 9 |
| 2.5 | 1 | 10 | 2 | 18 |
| 2.3 | 1 | 9 | 1 | 22 |
| 1.9 | 2 | 14 | 1 | 8 |
| 1.9 | 1 | 11 | 1 | 15 |
| 1.9 | 2 | 14 | 2 | 20 |
| 2.1 | 3 | 12 | 1 | 6 |
| 1.9 | 2 | 7 | 1 | 15 |
| 2.1 | 2 | 10 | 3 | 9 |
| 2.1 | 3 | 12 | 2 | 19 |
| 2.0 | 1 | 8 | 2 | 14 |
| 2.6 | 2 | 8 | 2 | 13 |
| 2.6 | 1 | 9 | 1 | 9 |
| 2.0 | 1 | 7 | 2 | 11 |
| 2.6 | 1 | 12 | 3 | 7 |
| 1.9 | 2 | 9 | 1 | 11 |
| 2.5 | 3 | 7 | 2 | 7 |
| 2.1

### Types of Punishment

1. **Probation/Community Service**
2. **Jail Incarceration**
3. **Prison Incarceration**

### Marital Status

1. **Married**
2. **Single**
3. **Other**

This chart is a classification system for types of punishment and marital status, using numerical identifiers for each category. It is organized into two sections: "Type of Punishment" and "Marital Status," each listing options with corresponding numbers for easy reference in data analysis or educational purposes.

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 + ...

Expert Solution

Step 1

The 99% confidence interval for the the population mean years of education, will signify that, with 99% confidence the population mean years of education lies within that interval. If $(a, b)$ denotes the 99% confidence interval, then a will be the lower limit and b will be the upper limit.

Since, population standard deviation is unknown, the sampling distribution can be assumed to follow student-t distribution and further t-confidence interval formula will be appropriate in this case.