The average final exam score for the statistics course is 74%. A professor wants to see if the average final exam score for students who are given colored pens on the first day of class is different. The final exam scores for the 16 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal.
The average final exam score for the statistics course is 74%. A professor wants to see if the average final exam score for students who are given colored pens on the first day of class is different. The final exam scores for the 16 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal.
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![### Hypothesis Testing for Mean Difference
The average final exam score for the statistics course is 74%. A professor wants to see if the average final exam score for students who are given colored pens on the first day of class is different. The final exam scores for the 16 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal.
**Final Exam Scores:**
67, 76, 73, 76, 68, 72, 61, 65, 71, 70, 54, 70, 72, 53, 59, 67
**What can be concluded at the \(\alpha = 0.05\) level of significance?**
#### Questions:
**a. For this study, we should use \_\_\_\_\_\_\_\_\_\_**
- [Select an answer]
**b. The null and alternative hypotheses would be:**
\[ H_0 : \] [Select an answer]
\[ H_1 : \] [Select an answer]
**c. The test statistic \[?\] =** \_\_\_\_\_\_
- (please show your answer to 3 decimal places).
**d. The p-value =** \_\_\_\_\_\_
- (Please show your answer to 4 decimal places.)
**e. The p-value is \[? \alpha \]
**f. Based on this, we should \_\_\_\_
- [Select an answer] the null hypothesis.
**g. Thus, the final conclusion is that ...**
- [ ] The data suggest the population mean is significantly different from 74 at \(\alpha = 0.05\), so there is statistically significant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is different from 74.
- [ ] The data suggests that the population mean final exam score for students who are given colored pens at the beginning of class is not significantly different from 74 at \(\alpha = 0.05\), so there is statistically insignificant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is different from 74.
- [ ] The data suggest the population mean is not significantly different from 74 at \(\alpha = 0.05\), so there](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fadb58edc-76a8-4215-8abd-8e37e0700ca4%2Ff579aed6-97bd-43b4-8723-a6b7d3c03859%2Fkv7go8u.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for Mean Difference
The average final exam score for the statistics course is 74%. A professor wants to see if the average final exam score for students who are given colored pens on the first day of class is different. The final exam scores for the 16 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal.
**Final Exam Scores:**
67, 76, 73, 76, 68, 72, 61, 65, 71, 70, 54, 70, 72, 53, 59, 67
**What can be concluded at the \(\alpha = 0.05\) level of significance?**
#### Questions:
**a. For this study, we should use \_\_\_\_\_\_\_\_\_\_**
- [Select an answer]
**b. The null and alternative hypotheses would be:**
\[ H_0 : \] [Select an answer]
\[ H_1 : \] [Select an answer]
**c. The test statistic \[?\] =** \_\_\_\_\_\_
- (please show your answer to 3 decimal places).
**d. The p-value =** \_\_\_\_\_\_
- (Please show your answer to 4 decimal places.)
**e. The p-value is \[? \alpha \]
**f. Based on this, we should \_\_\_\_
- [Select an answer] the null hypothesis.
**g. Thus, the final conclusion is that ...**
- [ ] The data suggest the population mean is significantly different from 74 at \(\alpha = 0.05\), so there is statistically significant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is different from 74.
- [ ] The data suggests that the population mean final exam score for students who are given colored pens at the beginning of class is not significantly different from 74 at \(\alpha = 0.05\), so there is statistically insignificant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is different from 74.
- [ ] The data suggest the population mean is not significantly different from 74 at \(\alpha = 0.05\), so there
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