MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### 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.
expand button
Transcribed Image Text:### 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.
expand button
Transcribed Image Text:### 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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