Question

# of OpenLab visits	Final grade
2	40
8	85
10	80
9	84
15	90
7	72
5	50
4	59
8	85
10	70
7	66
7	70
5	63
4	60
4	59
11	79
3	82
9	90
10	82
9	76
14	85
6	73
5	41
4	56
8	80
10	70
7	66
9	88
5	65
4	70
4	62
11	90

In what follows use any of the following tests/procedures: Regression, confidence intervals, one-sided t-test, or two-sided t-test. The procedures should be done with 5% P-value or 95% confidence interval.

Open Lab Visits data. Is it reasonable to claim that students with 8 or more visits to open lab sessions have average final grade higher than students with less than 8 visits?

1. What test/procedure did you perform? (5 points)

• a. One-sided t-test
• b. Two-sided t-test
• c. Regression
• d. Confidence Interval

2. Why did you choose this test/procedure? Because… (5 points)

• a. We are checking if number of visits influences final grade.
• b. We are checking if two averages are significantly different.
• c. We are checking if the average of one variable is larger than the average of the other variable.
• d. We are comparing the average final grade with a specific number.

3. What is the P-value/margin of error? (5 points)

• a. 7.19248E-07
• b. 3.59609E-07
• c. 2.55531E-06
• d. 4.161353

4. What is the Statistical interpretation? (5 points)

• a. The P-value is much smaller than 5% thus we are very certain that the slope is not zero.
• b. The P-value is much smaller than 5% thus the test result is conclusive.
• c. The P-value is much smaller than 5% thus we can claim that the number of visits to open lab sessions is related to final grade.
• d. The prediction interval for the true average final grade of students with 8 or more visits to open lab is [78.64454, 85.88879]

5. What is the conclusion? (5 points)

• a. We are confident that more visits to open lab sessions lead to higher final grades.
• b. We are confident that students with 8 or more visits to open lab sessions have average final grade greater than students with less than 8 visits.
• c. We are NOT confident that students with 8 or more visits to open lab sessions have average final grade greater than students with less than 8 visits.
• d. None of these.

Answer 1

1:

Here we have two independent samples and we need to find whether one average is greater than other so one side t test will be used.

Correct option is a.

2:

c. We are checking if the average of one variable is larger than the average of the other variable.

3:

Following are the two data sets:

less than 8 visitis	Final grade, X1	8 or more visits	Final grade, X2
2	40	8	85
3	82	8	85
4	59	8	80
4	60	9	84
4	59	9	90
4	56	9	76
4	70	9	88
4	62	10	80
5	50	10	70
5	63	10	82
5	41	10	70
5	65	11	79
6	73	11	90
7	72	14	85
7	66	15	90
7	70
7	66

Following is the output of t test generated by excel:

Correct option is b. 3.59609E-07.

(4)

Correct option:

b. The P-value is much smaller than 5% thus the test result is conclusive.

(5)

b. We are confident that students with 8 or more visits to open lab sessions have average final grade greater than students with less than 8 visits.