Question

The following table shows the grades (out of 100) for a sample of 8 randomly chosen students on two consecutive exams. Construct the 90% confidence interval for the difference of mean grades on the two exams. Round your answer to 2 decimal places. Can it be concluded that the grades on the second test were significantly different from the first one?

Student #: 1 2 3 4 5 6 7 8

Test 1: 67 88 76 88 91 95 79 71

Test 2: 69 78 76 84 86 96 70 68

Answer #1

Confidence interval for difference between two population means of paired samples is given as below:

Confidence interval = Dbar ± t*S_{D}/sqrt(n)

From given data, we have

Dbar = 3.5

S_{d} = 4.440077219

n = 8

df = n – 1 = 7

Confidence level = 90%

Critical t value = 1.8946

(by using t-table)

Confidence interval = Dbar ± t*S_{D}/sqrt(n)

Confidence interval = 3.5 ± 1.8946*4.440077219/sqrt(8)

Confidence interval = 3.5 ± 1.8946*1.569804355

Confidence interval = 3.5 ± 2.9741

Lower limit = 3.5 - 2.9741 = 0.53

Upper limit = 3.5 + 2.9741 =6.47

0.53 < µ_{d} < 6.47

It can be concluded that the grades on the second test were significantly different from the first one, because the above interval do not contain the value zero.

Student Grades
Student
Test
Grade
1
76
62
2
84
90
3
79
68
4
88
84
5
76
58
6
66
79
7
75
73
8
94
93
9
66
65
10
92
86
11
80
53
12
87
83
13
86
49
14
63
72
15
92
87
16
75
89
17
69
81
18
92
94
19
79
78
20
60
71
21
68
84
22
71
74
23
61
74
24
68
54
25
76
97...

Using the accompanying Student Grades data, construct a scatter
chart for midterm versus final exam grades and add a linear
trendline. What is the model? If a student scores 7878 on the
midterm, what would you predict her grade on the final exam to
be?
Student
Midterm
Final Exam
1
75
64
2
85
91
3
80
68
4
88
83
5
76
60
6
67
80
7
78
74
8
95
94
9
67
61
10
93
87
11...

Below represent scores on an exam, each entry one score for one
student
40
99
59
98
63
63
64
65
67
35
67
67
68
70
71
71
71
46
72
72
60
73
74
74
74
75
97
75
62
76
76
76
76
76
77
57
77
98
77
63
78
78
78
79
79
80
80
80
80
80
81
81
92
81
93
82
82
83
83
83
83
83
83
83
84
84
84...

The following scores represent a sample of final examination
grades for a statistics course
23 60 98 32 57 74 52 70 82 69 74 63 80 62 80 77 81 95 41 65 92
85 85 61 36 79 55 76 52 10 64 75 78 25 80 48 83 64 88 82 81 67 41
71 67 54 34 72 74 43 60 78 84 89 76 84 17 90 15 79
a) Compute the 20th percentile of...

Mid Score
Final Score
80
78
87
85
72
81
69
54
86
70
83
73
78
89
75
84
74
86
75
79
84
75
73
63
74
72
73
69
80
86
75
78
72
75
77
68
76
77
66
78
74
77
71
73
85
79
74
74
76
79
76
73
84
72
77
81
78
86
86
76
81
83
78
83
85
86
73
71
83
83
83
79
72
68
83
90...

Sample scores from four different statistics class sections are
shown below. Run an ANOVA test on them and answer the following
questions:
Class 1
Class 2
Class 3
Class 4
95
79
77
81
99
68
91
96
75
84
84
68
76
78
84
89
82
74
75
78
97
93
82
75
93
95
82
88
83
88
85
98
86
95
96
59
What conclusion can we make about the hypothesis test?

The data file ExxamScores shows the 40 students
in a TOM 3010 course exxam scores for the Middtermm and Final
exxam. Is there statistically significant evidence to show that
students score lower on their final exxam than middtermm exxam?
Provide the p-value for this analysis.ROUND TO 4 DECIMAL
PLACES.
ExxamScores
Student ID #
Middtermmm
Final
56065
97
64
79499
95
85
59716
89
72
83504
79
64
77735
78
74
57760
87
93
78204
83
70
81177
94
79
54398...

The following scores represent a sample of final examination
grades for a statistics course
23 60 98 32 57 74 52 70 82 69 74 63 80 62 80 77 81 95 41 65 92
85 85 61 36 79 55 76 52 10 64 75 78 25 80 48 83 64 88 82 81 67 41
71 67 54 34 72 74 43 60 78 84 89 76 84 17 90 15 79
a) Provide a frequency polygon with...

The Test Scores for a Statistics course are given in the Excel
below.
The data (X1, X2, X3, X4) are for each student.
X1 = score on exam #1
X2 = score on exam #2
X3 = score on exam #3
X4 = score on final exam
Your professor wants to know if all tests are created equal.
What is the F-Stat?
EXAM1
EXAM2
EXAM3
FINAL
73
80
75
65.86667
93
88
93
80.16667
89
91
90
78
96
98...

Question 9-15 are based on the random
sample below which is obtained to test the following hypothesis
about the population mean. Test the hypothesis that the mean is
less than 80.
80
100
81
93
80
57
98
90
71
56
58
78
59
55
55
77
72
78
56
94
98
59
93
86
89
62
60
66
59
71
96
97
94
69
64
77
87
77
64
90
90
95
98
99
56
69
72
81
95...

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