Statistical Inference: Exam Score Comparison Methods

STAT 302 - Fall 2023 Week In Review Dr. Mohamed Aburweis Copyright © 2023 Aburweis Note # 10 Page 1 of 8 Note # 10: Statistical Inference for Numerical Variables Problem 1. A statistics professor at a large community college wanted to determine if there was a difference in the means of the final exam scores between students who took his statistics course online and the students who took his course face-to-face. He randomly selected 30 students from his online course. The average exam score in this group was an 85.6, with a standard deviation of 4.3. He randomly selected 30 students from his face-to-face course. The average exam score in this group was an 83.2, with a standard deviation of 2.7. Create a 98% confidence interval for the difference between the average grade of the face-to-face group versus the online group. a. Construct the 98% confidence interval. b. Interpret your confidence interval from part a.

STAT 302 - Fall 2023 Week In Review Dr. Mohamed Aburweis Copyright © 2023 Aburweis Note # 10 Page 2 of 8 Problem 2. A statistics professor at a large community college wanted to determine if there was a difference in the means of the final exam scores between students who took his statistics course online and the students who took his course face-to-face. He randomly selected 30 students from his online course. The average exam score in this group was an 85.6, with a standard deviation of 4.3. He randomly selected 30 students from his face-to-face course. The average exam score in this group was an 83.2, with a standard deviation of 2.7. Conduct a hypothesis test at the 0.02 significance level to test this. a. What are the hypotheses? b. What is the significance level? c. What is the value of the test statistic? d. What is the p-value? e. What is the correct decision? f. What is the appropriate conclusion/interpretation? g. Does the hypothesis test agree with the confidence interval from question 1?

STAT 302 - Fall 2023 Week In Review Dr. Mohamed Aburweis Copyright © 2023 Aburweis Note # 10 Page 3 of 8 Problem 3. An instructor decided to create two different versions of the same exam, Version A and Version B. Prior to passing out the exams, he shuffled the exams together to ensure each student received a random version. Of the 30 students who took Version A, the average score was a 79.4, with a standard deviation of 14. Of the 27 students who took Version B, the average score was a 74.1, with a standard deviation of 20. Because he wants to ensure that the exam was fair to all students, he would like to evaluate whether the difference observed in the groups is so large that it provided convincing evidence that Version B was more difficult (on average) than Version A. Consider the students who took Version A to be Group A and the students who took Version B to be Group B. Create a 99% confidence interval for the difference between the average scores on Version A and Version B. a. Construct the 90% confidence interval. b. Interpret your confidence interval from part a.

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STAT 302 - Fall 2023 Week In Review Dr. Mohamed Aburweis Copyright © 2023 Aburweis Note # 10 Page 4 of 8 Problem 4. An instructor decided to create two different versions of the same exam, Version A and Version B. Prior to passing out the exams, he shuffled the exams together to ensure each student received a random version. Of the 30 students who took Version A, the average score was a 79.4, with a standard deviation of 14. Of the 27 students who took Version B, the average score was a 74.1, with a standard deviation of 20. Because he wants to ensure that the exam was fair to all students, he would like to evaluate whether the difference observed in the groups is so large that it provided convincing evidence that Version B was more difficult (on average) than Version A. Consider the students who took Version A to be Group A and the students who took Version B to be Group B. Conduct a hypothesis test at the 0.01 significance level to test this. a. What are the hypotheses? b. What is the significance level? c. What is the value of the test statistic? d. What is the p-value? e. What is the correct decision? f. What is the appropriate conclusion/interpretation? g. Does the hypothesis test agree with the confidence interval from question 3?

STAT 302 - Fall 2023 Week In Review Dr. Mohamed Aburweis Copyright © 2023 Aburweis Note # 10 Page 5 of 8 Problem 5. Use the following ANOVA output to answer the questions below. Assume we are conducting this test at the 10% level. Source DF Sum of Squares Mean Squares F Value Prob Groups 2 435.59259 217.7963 1.9211042 0.1569 Error (Residuals) 51 5781.8889 113.37037 Total 53 6217.4815 a. Based on the type of test that was run, what kind of variables are we studying? b. How many groups were compared? c. How many total observations were there? d. What is the SSG? What is the SSE? What is the SST? e. What is the MSG? What is the MSE? f. What is the value of the test statistic? g. What is the p-value? h. What is the correct decision? i. What is the appropriate conclusion/interpretation?

STAT 302 - Fall 2023 Week In Review Dr. Mohamed Aburweis Copyright © 2023 Aburweis Note # 10 Page 6 of 8 Problem 6. Use the following data set, and create and compute the values for the ANOVA table. Group 1 Group 2 Group 3 11 7 15 10 8 17 11 16 ANOVA Table: Source DF Sum of Squares Mean Squares F Value Prob Groups 0.000193 Error (Residuals) Total

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STAT 302 - Fall 2023 Week In Review Dr. Mohamed Aburweis Copyright © 2023 Aburweis Note # 10 Page 7 of 8 Problem 7. A teacher wants to know if test scores are different between his classes. Test this at the 5% level. Source DF Sum of Squares Mean Squares F Value Prob Class (Groups) 3 3.798 0.066358 Error (Residuals) 41.228 Total 84 a. What kind of test should we conduct? b. What are the hypotheses? c. What is the significance level? d. The ANOVA table above is partially filled in. Complete the missing spaces. e. How many different classes was the teacher comparing? f. How many total students were in those classes? g. What is the value of the test statistic? h. What is the p-value? i. What is the correct decision? j. What is the appropriate conclusion/interpretation?

STAT 302 - Fall 2023 Week In Review Dr. Mohamed Aburweis Copyright © 2023 Aburweis Note # 10 Page 8 of 8 Problem 8. A commuter thinks that the time it takes them to commute is different based on what day of the week it is. For a few weeks, they record their commute time each day, Monday through Friday. Test their claim at the 5% level. Source DF Sum of Squares Mean Squares F Value Prob Day (Groups) 14.28 0.037122 Error (Residuals) Total 19 30.2 a. What kind of test should we conduct? b. What are the hypotheses? c. What is the significance level? d. The ANOVA table above is partially filled in. Complete the missing spaces. e. What is the value of the test statistic? f. What is the p-value? g. What is the correct decision? h. What is the appropriate conclusion/interpretation?

WIR_23C_S302_H10

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