### Task OverviewThe exercise involves using statistical methods to analyze data for educational purposes, specifically finding sample means and confidence intervals.#### Data and TaskA sample of annual earnings (in thousands of dollars) from 15 microbiologists has been provided. The objective is:1. **Find the sample mean** of the data.2. **Construct a 99% confidence interval** for the mean of the population. Assume the sample's standard deviation is representative of the population's standard deviation.#### Data PointsThe earnings data for the microbiologists are as follows (in thousands of dollars):- 66- 73- 58- 41- 62- 41- 52- 55- 66- 77- 63- 49- 57- 56- 68#### Questions1. (A) Calculate the sample mean. 2. (B) Calculate the 99% confidence interval for the population mean.For the calculations, the sample mean is to be rounded to two decimal places.### InstructionsEnter the calculated answers in the answer box and click "Check Answer" to verify your responses. ### Sample Mean CalculationIn this exercise, we will calculate the sample mean from a set of data points. The data points provided are:```100,328, 80,676, 78,344, 67,552, 51,806, 67,447, 94,688, 65,72879,537, 73,501, 44,328, 87,224, 60,548, 58,256, 55,056, 77,78647,594, 98,728, 81,492, 92,605, 63,891, 74,013, 50,948, 60,52591,553, 84,457, 80,441, 64,033, 74,365, 57,304, 47,192, 89,84175,278, 62,238, 82,906```#### Task(a) Find the sample mean.#### Procedure1. **Sum the Data Points**: Add all the numbers together.2. **Count the Data Points**: Determine how many data points there are.3. **Calculate the Mean**: Divide the sum of the data points by the number of points.#### FormulaThe formula to calculate the sample mean ($\bar{x}$) is:\[\bar{x} = \frac{\sum x_i}{n}\]where $\sum x_i$ is the sum of all data points and $n$ is the number of data points.#### Input- Enter the calculated mean in the provided answer box.- Remember to round the result to two decimal places as needed.#### Instructions1. Enter your answer in the answer box.2. Click "Check Answer" to validate your response.#### Progress TrackingThe progress bar will update as you complete different parts of the task.

Name: ### Task OverviewThe exercise involves using statistical methods to a
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Description: ### Task OverviewThe exercise involves using statistical methods to analyze data for educational purposes, specifically finding sample means and confidence intervals.#### Data and TaskA sample of annual earnings (in thousands of dollars) from 15 mic

Number of samples (n) = 35 Let "X" be the annual earnings. 100,328 80,676 78,344 67,552 51,806 67,447 94,688 65,728 79,537 73,501 44,328 87,224 60,548 58,256 55,056 77,786 47,594 98,728 81,492 92,605 63,891 74,013 50,948 60,525 91,553 84,457 80,441 64,033 74,365 57,304 47,192 89,841 75,278 62,238 82,906 Plug in all the values in the formula, we get Round to two decimal places (Nearest hundredth).

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The annual earnings (in dollars) of 35 randomly selected microbiologists are shown in the data table. Use the data to (a) find the sample mean, (b) find the sample standard deviation, and (c) construct a 98% confidence interval for the population mean. 100,328 80,676 78,344 67,552 51,806 67,447 94,688 65,728 D 79,537 73,501 44,328 87,224 47,594 98,728 81,492 92,605 63,891 74,013 50,948 60,548 58,256 55,056 77,786 60,525 (a) Find the sample mean. (Type an integer or decimal rounded to two decimal places as needed.) Enter your answer in the answer box and then click Check Answer. parts Clear All

The annual earnings (in dollars) of 35 randomly selected microbiologists are shown in the data table. Use the data to (a) find the sample mean, (b) find the sample standard deviation, and (c) construct a 98% confidence interval for the population mean. 100,328 80,676 78,344 67,552 51,806 67,447 94,688 65,728 D 79,537 73,501 44,328 87,224 47,594 98,728 81,492 92,605 63,891 74,013 50,948 60,548 58,256 55,056 77,786 60,525 (a) Find the sample mean. (Type an integer or decimal rounded to two decimal places as needed.) Enter your answer in the answer box and then click Check Answer. parts Clear All

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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Topic Video

Question

### Task Overview

The exercise involves using statistical methods to analyze data for educational purposes, specifically finding sample means and confidence intervals.

#### Data and Task

A sample of annual earnings (in thousands of dollars) from 15 microbiologists has been provided. The objective is:

1. **Find the sample mean** of the data.
2. **Construct a 99% confidence interval** for the mean of the population. Assume the sample's standard deviation is representative of the population's standard deviation.

#### Data Points

The earnings data for the microbiologists are as follows (in thousands of dollars):

- 66
- 73
- 58
- 41
- 62
- 41
- 52
- 55
- 66
- 77
- 63
- 49
- 57
- 56
- 68

#### Questions

1. (A) Calculate the sample mean.
2. (B) Calculate the 99% confidence interval for the population mean.

For the calculations, the sample mean is to be rounded to two decimal places.

### Instructions

Enter the calculated answers in the answer box and click "Check Answer" to verify your responses.

### Sample Mean Calculation

In this exercise, we will calculate the sample mean from a set of data points. The data points provided are:

```
100,328, 80,676, 78,344, 67,552, 51,806, 67,447, 94,688, 65,728
79,537, 73,501, 44,328, 87,224, 60,548, 58,256, 55,056, 77,786
47,594, 98,728, 81,492, 92,605, 63,891, 74,013, 50,948, 60,525
91,553, 84,457, 80,441, 64,033, 74,365, 57,304, 47,192, 89,841
75,278, 62,238, 82,906
```

#### Task
(a) Find the sample mean.

#### Procedure
1. **Sum the Data Points**: Add all the numbers together.
2. **Count the Data Points**: Determine how many data points there are.
3. **Calculate the Mean**: Divide the sum of the data points by the number of points.

#### Formula
The formula to calculate the sample mean ($\bar{x}$) is:
\[
\bar{x} = \frac{\sum x_i}{n}
\]
where $\sum x_i$ is the sum of all data points and $n$ is the number of data points.

#### Input
- Enter the calculated mean in the provided answer box.
- Remember to round the result to two decimal places as needed.

#### Instructions
1. Enter your answer in the answer box.
2. Click "Check Answer" to validate your response.

#### Progress Tracking
The progress bar will update as you complete different parts of the task.

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