An online math tutor service would like to claim that the average time spent taking a standardized test after students go through tutoring is less than the average time spent before going through tutoring. A simple random sample of students takes a pre-test, then goes through tutoring and takes a post-test. Results of the sample are shown below. What are the population parameters? Mean Variance Before After 79.278 75.556 126.448 125.203 18 0.521 Observations 18 Pick Pearson Correlation Hypothesized Mean Difference 0 Is the two-sample hypothesis test a paired t-test or an unpaired t-test? df 17 t Stat -1.438 P(T

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### Hypothesis Tests for the Difference Between Two Population Means

An online math tutor service would like to claim that the average time spent taking a standardized test after students go through tutoring is less than the average time spent before going through tutoring. A simple random sample of students takes a pre-test, then goes through tutoring, and takes a post-test. Results of the sample are shown below.

|                 | Before    | After     |
|-----------------|-----------|-----------|
| Mean            | 79.278    | 75.556    |
| Variance        | 126.448   | 755.203   |
| Observations    | 18        | 18        |
| Pearson Correlation | 0.521   |           |
| Hypothesized Mean Difference |          | 0         |
| df              |           | 17        |
| t Stat          |           | 1.438     |
| P(T<=t) one-tail|           | 0.084     |
| t Critical one-tail |       | 1.740     |
| P(T<=t) two-tail|           | 0.169     |
| t Critical two-tail |       | 2.110     |
| Confidence Level|           | 95%       |

### Key Questions:

1. **What are the population parameters?**
2. **Is the two-sample hypothesis test a paired \( t \)-test or an unpaired \( t \)-test?**
3. **What is the level of significance?** (Example: 0.12)
4. **What is the null hypothesis \( H_0 \)?**
5. **What is the alternative hypothesis \( H_a \)?**
6. **Should \( H_0 \) be rejected or does \( H_0 \) fail to be rejected?**
7. **What conclusion can be drawn from the data?**

### Possible Answers:

1. **Population Parameters: Select from the drop-down menu.**
2. **Type of \( t \)-test: Select either paired or unpaired from the drop-down menu.**
3. **Level of Significance: Input the value (Example: 0.12).**
4. **Null Hypothesis \( H_0 \)**
   - [Select option]
5. **Alternative Hypothesis \( H_a \)**
   - [Select option]
6. **Decision on \( H_0 \)
Transcribed Image Text:### Hypothesis Tests for the Difference Between Two Population Means An online math tutor service would like to claim that the average time spent taking a standardized test after students go through tutoring is less than the average time spent before going through tutoring. A simple random sample of students takes a pre-test, then goes through tutoring, and takes a post-test. Results of the sample are shown below. | | Before | After | |-----------------|-----------|-----------| | Mean | 79.278 | 75.556 | | Variance | 126.448 | 755.203 | | Observations | 18 | 18 | | Pearson Correlation | 0.521 | | | Hypothesized Mean Difference | | 0 | | df | | 17 | | t Stat | | 1.438 | | P(T<=t) one-tail| | 0.084 | | t Critical one-tail | | 1.740 | | P(T<=t) two-tail| | 0.169 | | t Critical two-tail | | 2.110 | | Confidence Level| | 95% | ### Key Questions: 1. **What are the population parameters?** 2. **Is the two-sample hypothesis test a paired \( t \)-test or an unpaired \( t \)-test?** 3. **What is the level of significance?** (Example: 0.12) 4. **What is the null hypothesis \( H_0 \)?** 5. **What is the alternative hypothesis \( H_a \)?** 6. **Should \( H_0 \) be rejected or does \( H_0 \) fail to be rejected?** 7. **What conclusion can be drawn from the data?** ### Possible Answers: 1. **Population Parameters: Select from the drop-down menu.** 2. **Type of \( t \)-test: Select either paired or unpaired from the drop-down menu.** 3. **Level of Significance: Input the value (Example: 0.12).** 4. **Null Hypothesis \( H_0 \)** - [Select option] 5. **Alternative Hypothesis \( H_a \)** - [Select option] 6. **Decision on \( H_0 \)
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