A sample of 8 people participated in a low calorie weight loss program for 16 weeks. Each of the participants had their weight (in pounds) recorded before they started the program and after they finished the program. The following results were obtained.At the 0.05 level of significance, test the claim that, on average, this 16 week low calorie weight loss program is effective? Assume that the amount of weight people lose after 16 weeks participating in this low calorie weight loss program reasonably follows a normal distribution. The table displayed shows the weights of eight participants before and after a certain period or activity, possibly suggesting a study on weight change.| Participant | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 ||-------------|-----|-----|-----|-----|-----|-----|-----|-----|| Weight Before | 187 | 243 | 168 | 203 | 159 | 215 | 230 | 196 || Weight After | 172 | 222 | 151 | 175 | 146 | 207 | 206 | 177 |**Explanation:**- **Participants:** There are eight different individuals, labeled from 1 to 8.- **Weight Before:** This row shows the weight of each participant before the intervention or study. The weights range from 159 to 243.- **Weight After:** This row lists the weight of each participant after the intervention or study. The weights range from 146 to 222. This data could be used to analyze the effectiveness of a weight loss program, showing the decrease in weight for each participant.

Null Hypothesis: H0: The average calorie weight loss program is not effective. Alternative…

Answered: A sample of 8 people participated in a…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 27SGR

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A sample of 8 people participated in a low calorie weight loss program for 16 weeks. Each of the participants had their weight (in pounds) recorded before they started the program and after they finished the program. The following results were obtained.

At the 0.05 level of significance, test the claim that, on average, this 16 week low calorie weight loss program is effective? Assume that the amount of weight people lose after 16 weeks participating in this low calorie weight loss program reasonably follows a normal distribution.

The table displayed shows the weights of eight participants before and after a certain period or activity, possibly suggesting a study on weight change.

| Participant | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|-------------|-----|-----|-----|-----|-----|-----|-----|-----|
| Weight Before | 187 | 243 | 168 | 203 | 159 | 215 | 230 | 196 |
| Weight After | 172 | 222 | 151 | 175 | 146 | 207 | 206 | 177 |

**Explanation:**

- **Participants:** There are eight different individuals, labeled from 1 to 8.
- **Weight Before:** This row shows the weight of each participant before the intervention or study. The weights range from 159 to 243.
- **Weight After:** This row lists the weight of each participant after the intervention or study. The weights range from 146 to 222.

This data could be used to analyze the effectiveness of a weight loss program, showing the decrease in weight for each participant.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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