A teacher wants to see if a new unit on taking square roots is helping students learn. She has five randomly selected students take a pre-test and a post-test on the material. The scores are out of 20. Has there been improvement?

Student Scores:

| Student | Pre-test | Post-test |
|---------|----------|-----------|
| 1 | 11 | 18 |
| 2 | 9 | 17 |
| 3 | 10 | 19 |
| 4 | 14 | 20 |
| 5 | 10 | 18 |

The test statistic is -14.9.

What is the p-value?

A. p-value > 0.01
B. p-value > 0.02
C. p-value < 0.001
D. p-value < 0.002

The p-value being asked for represents the probability that the improvement in test scores is due to chance. Given the information, it indicates a significant improvement in scores after the new square root unit, suggesting a p-value of less than 0.001.

Explanation:

The p-value is a measure of the probability that an observed difference could have occurred just by random chance. In this case, the teacher has recorded pre- and post-test scores for a new unit on taking square roots. The test statistic has been calculated as -14.9, which represents the overall difference in scores before and after the test.

To interpret the p-value we compare it to a significance level, typically 0.05. In the provided choices the p-value is not exactly given, but we have ranges. The most common level, 0.05, is not represented in the options hence we have to base on what's given.

Depending on the variant of the t-test used to calculate this test statistic, the actual computation of the p-value can be complex. However, with such a large negative test statistic, we can infer that the p-value is going to be very small indicating a significant change. Thus, without the exact figures, a likely answer would be C) p-value < 0.001.

Learn more about p-value here:

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