What is the test statistic?

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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### Hypothesis Testing Worksheet

**a) State the null and alternative hypothesis – identify the order in which you are subtracting!**

- \( H_0 \): [Null Hypothesis]
- \( H_a \): [Alternative Hypothesis]

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

[Enter test statistic here]

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

[Enter p-value here]

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

[Enter conclusion here]
Transcribed Image Text:### Hypothesis Testing Worksheet **a) State the null and alternative hypothesis – identify the order in which you are subtracting!** - \( H_0 \): [Null Hypothesis] - \( H_a \): [Alternative Hypothesis] **b) What is the test statistic?** [Enter test statistic here] **c) What is the p-value?** [Enter p-value here] **d) State your conclusion (in the context of the problem).** [Enter conclusion here]
**IQ Test Results for Special Training Study**

**Study Design and Purpose:**
Forty-four sixth graders were randomly selected from a school district for an experiment designed to evaluate the effectiveness of special training on student performance. The students were paired into 22 matched pairs based on having equal IQ scores. One member of each pair was randomly assigned to receive special training, while the other member did not receive any training. All participants subsequently took an IQ test. The results are summarized in the table below. The primary question is whether the training had a significant effect on improving student performance on the IQ test. A significance level of 0.05 will be used for the analysis, and it is assumed that the mean differences in scores are approximately normally distributed.

**Test Results:**

|      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     |
|        87        |      83     |
|        85        |      83     |
|        85        |      82     |
|        68        |      65     |
|        81        |      79     |
|        84        |      83     |
|        71        |      60     |
|        46        |      47     |
|        75        |      77     |
|        80        |      83     |

**Interpretation:**
To determine if the special training provided any significant improvement in IQ test scores compared to the no-training group, a statistical test such as a paired t-test can be performed. The differences between the paired IQ scores will be analyzed, and the result will be compared against the 0.05 level of significance to infer if the training had a statistically significant effect on student performance.
Transcribed Image Text:**IQ Test Results for Special Training Study** **Study Design and Purpose:** Forty-four sixth graders were randomly selected from a school district for an experiment designed to evaluate the effectiveness of special training on student performance. The students were paired into 22 matched pairs based on having equal IQ scores. One member of each pair was randomly assigned to receive special training, while the other member did not receive any training. All participants subsequently took an IQ test. The results are summarized in the table below. The primary question is whether the training had a significant effect on improving student performance on the IQ test. A significance level of 0.05 will be used for the analysis, and it is assumed that the mean differences in scores are approximately normally distributed. **Test Results:** | 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 | | 87 | 83 | | 85 | 83 | | 85 | 82 | | 68 | 65 | | 81 | 79 | | 84 | 83 | | 71 | 60 | | 46 | 47 | | 75 | 77 | | 80 | 83 | **Interpretation:** To determine if the special training provided any significant improvement in IQ test scores compared to the no-training group, a statistical test such as a paired t-test can be performed. The differences between the paired IQ scores will be analyzed, and the result will be compared against the 0.05 level of significance to infer if the training had a statistically significant effect on student performance.
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