Forty- four sixth Graders were randomly selected for a school district. then they were divided into 22 to match pairs, each Paris having equal IQs. one member of each pier was randomly selected to receive special training. then all the students were giving an IQ test. test results are summarized below. Do these results provide evidence that the special training helped student performance? Use a 0.05 level of significance. Assume that the mean difference are approximately normally distributed. ### Comparison of Test Scores Between Training and No Training GroupsThe following table presents the scores obtained by two groups, one that underwent a training program and another that did not. Each row represents the scores of individual participants in both the training and no-training groups.| Training | No Training ||----------|--------------|| 95 | 90 || 89 | 85 || 76 | 73 || 92 | 90 || 91 | 90 || 53 | 53 || 67 | 68 || 88 | 90 || 75 | 78 || 85 | 89 || 90 | 95 || 85 | 83 || 85 | 82 || 68 | 65 || 81 | 79 || 84 | 83 || 71 | 60 || 46 | 47 || 75 | 77 || 80 | 83 |This dataset can be utilized to analyze the impact of training on performance by comparing the scores of participants in both groups. Potential analyses could include calculating the mean scores for each group, the median, and standard deviation, in addition to performing statistical tests such as a t-test to determine if the difference in performance is statistically significant. Visual representations such as bar graphs or box plots may also enhance the comparison and interpretation of these scores. ### Hypothesis Testing Worksheet#### a) State the null and alternative hypotheses – **identify the order in which you are subtracting!**- $ H_0 $:- $ H_a $:#### b) What is the test statistic?#### c) What is the p-value?#### d) State your conclusion (in the context of the problem).

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Forty- four sixth Graders were randomly selected for a school district. then they were divided into 22 to match pairs, each Paris having equal IQs. one member of each pier was randomly selected to receive special training. then all the students were giving an IQ test. test results are summarized below. Do these results provide evidence that the special training helped student performance? Use a 0.05 level of significance. Assume that the mean difference are approximately normally distributed.

### Comparison of Test Scores Between Training and No Training Groups

The following table presents the scores obtained by two groups, one that underwent a training program and another that did not. Each row represents the scores of individual participants in both the training and no-training groups.

| Training | No Training |
|----------|--------------|
| 95 | 90 |
| 89 | 85 |
| 76 | 73 |
| 92 | 90 |
| 91 | 90 |
| 53 | 53 |
| 67 | 68 |
| 88 | 90 |
| 75 | 78 |
| 85 | 89 |
| 90 | 95 |
| 85 | 83 |
| 85 | 82 |
| 68 | 65 |
| 81 | 79 |
| 84 | 83 |
| 71 | 60 |
| 46 | 47 |
| 75 | 77 |
| 80 | 83 |

This dataset can be utilized to analyze the impact of training on performance by comparing the scores of participants in both groups. Potential analyses could include calculating the mean scores for each group, the median, and standard deviation, in addition to performing statistical tests such as a t-test to determine if the difference in performance is statistically significant. Visual representations such as bar graphs or box plots may also enhance the comparison and interpretation of these scores.

### Hypothesis Testing Worksheet

#### a) State the null and alternative hypotheses – **identify the order in which you are subtracting!**
- $ H_0 $:
- $ H_a $:

#### b) What is the test statistic?

#### c) What is the p-value?

#### d) State your conclusion (in the context of the problem).

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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