A sample of 8 students were selected to test the effectiveness of a course designed to improve typing skills. Their typing scores before and after the course are recorded below. Suppose that we would like to test whether the course is effective (i.e., the mean after-score is higher than the mean before- score) at a=0.01. What is the critical value? Before 45 After 56 O-3.355 O-2.326 O-2.896 O-3.499 O-2.576 O-2.998 38 42 60 62 35 39 70 75 48 50 39 42 49 56

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**Assessment of Typing Course Effectiveness**

A sample of 8 students was selected to test the effectiveness of a course designed to improve typing skills. Their typing scores before and after the course are recorded below. Suppose that we would like to test whether the course is effective (i.e., the mean after-score is higher than the mean before-score) at α = 0.01. What is the critical value?

|         | Before | After |
|---------|--------|-------|
| Student 1 | 45     | 56    |
| Student 2 | 38     | 42    |
| Student 3 | 60     | 62    |
| Student 4 | 35     | 39    |
| Student 5 | 70     | 75    |
| Student 6 | 48     | 50    |
| Student 7 | 39     | 42    |
| Student 8 | 49     | 56    |

**Options for Critical Value:**

- -3.355
- -2.326
- -2.896
- -3.499
- -2.576
- -2.998

**Explanation:**

To determine the effectiveness of the typing course, we conduct a hypothesis test. The null hypothesis (H₀) assumes there is no improvement (mean after-score is not higher than the mean before-score), while the alternative hypothesis (H₁) assumes there is an improvement. The provided responses represent possible critical values for this test based on the significance level α = 0.01.

If the test statistic (calculated from the data) is greater than the critical value, we reject the null hypothesis, indicating that the course is effective.

This exercise involves applying statistical methods to analyze and interpret the data, aiding in educational research and decision-making.
Transcribed Image Text:**Assessment of Typing Course Effectiveness** A sample of 8 students was selected to test the effectiveness of a course designed to improve typing skills. Their typing scores before and after the course are recorded below. Suppose that we would like to test whether the course is effective (i.e., the mean after-score is higher than the mean before-score) at α = 0.01. What is the critical value? | | Before | After | |---------|--------|-------| | Student 1 | 45 | 56 | | Student 2 | 38 | 42 | | Student 3 | 60 | 62 | | Student 4 | 35 | 39 | | Student 5 | 70 | 75 | | Student 6 | 48 | 50 | | Student 7 | 39 | 42 | | Student 8 | 49 | 56 | **Options for Critical Value:** - -3.355 - -2.326 - -2.896 - -3.499 - -2.576 - -2.998 **Explanation:** To determine the effectiveness of the typing course, we conduct a hypothesis test. The null hypothesis (H₀) assumes there is no improvement (mean after-score is not higher than the mean before-score), while the alternative hypothesis (H₁) assumes there is an improvement. The provided responses represent possible critical values for this test based on the significance level α = 0.01. If the test statistic (calculated from the data) is greater than the critical value, we reject the null hypothesis, indicating that the course is effective. This exercise involves applying statistical methods to analyze and interpret the data, aiding in educational research and decision-making.
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