Question

As part of its freshman orientation process, a college gives a math placement exam to incoming freshmen. The math department is interested in whether there is a statistically significant difference in the average exam score for students in different programs, at a level of α=0.01. The exam scores for random samples of science, engineering, humanities, and business majors are shown in the following table. The math department has confirmed that the samples were randomly selected and independent, that the populations are normally distributed, and that the population variances of scores are equal. Use a TI-83, TI-83 plus, or TI-84 calculator and the following table of critical values for the F-distribution to calculate the degrees of freedom, critical value, and test statistic for the data set, rounding the test statistic to two decimal places.

Critical Values of the F-Distribution for α=0.01

Degrees of Freedom for the Numerator | |||||

Degrees of Freedom for the Denominator |
1 | 2 | 3 | 4 | 5 |

30 | 7.56 | 5.39 | 4.51 | 4.02 | 3.70 |

31 | 7.53 | 5.36 | 4.48 | 3.99 | 3.67 |

32 | 7.50 | 5.34 | 4.46 | 3.97 | 3.65 |

33 | 7.47 | 5.31 | 4.44 | 3.95 | 3.63 |

34 | 7.44 | 5.29 | 4.42 | 3.93 | 3.61 |

35 | 7.42 | 5.27 | 4.40 | 3.91 | 3.59 |

36 | 7.40 | 5.25 | 4.38 | 3.89 | 3.57 |

37 | 7.37 | 5.23 | 4.36 | 3.87 | 3.56 |

38 | 7.35 | 5.21 | 4.34 | 3.86 | 3.54 |

39 | 7.33 | 5.19 | 4.33 | 3.84 | 3.53 |

40 | 7.31 | 5.18 | 4.31 | 3.83 | 3.51 |

Science |
Engineering |
Humanities |
Business |

87 |
88 |
85 |
82 |

79 |
89 |
84 |
78 |

84 |
88 |
91 |
80 |

83 |
86 |
84 |
78 |

89 |
89 |
83 |
78 |

87 |
87 |
79 |
79 |

91 |
94 |
91 |
74 |

83 |
90 |
81 |
79 |

85 |
86 |
82 |
83 |

86 |
86 |
91 |
79 |

Provide your answer below:

Numerator degrees of freedom = , denominator degrees of freedom = , critical value = , test statistic =

Answer #1

using excel>data>data analysis>one way anova

we have

Anova: Single Factor | ||||||

SUMMARY | ||||||

Groups | Count | Sum | Average | Variance | ||

Science | 10 | 854 | 85.4 | 11.6 | ||

Engineering | 10 | 883 | 88.3 | 6.011111 | ||

Humanities | 10 | 851 | 85.1 | 19.43333 | ||

Business | 10 | 790 | 79 | 6 | ||

ANOVA | ||||||

Source of Variation | SS | df | MS | F | P-value | F crit |

Between Groups | 458.5 | 3 | 152.8333 | 14.20237 | 2.89E-06 | 4.377 |

Within Groups | 387.4 | 36 | 10.76111 | |||

Total | 845.9 | 39 |

Numerator degrees of freedom =3

, denominator degrees of freedom = 36

, critical value =4.38

, test statistic =14.20

As part of its freshman orientation process, a college gives a
math placement exam to incoming freshmen. The math department is
interested in whether there is a statistically significant
difference in the average exam score for students in different
programs, at a level of α=0.01 . The exam scores for random samples
of science, engineering, humanities, and business majors are shown
in the following table. The math department has confirmed that the
samples were randomly selected and independent, that the...

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 on the midterm exam in a math
class were recorded. Find IQR. 93 81 59 69 82 73 61 77 95 84 88 71
85 97 63 72 89 80 60 98 91 62 78 83 76 81 94 66 83 96

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...

Daughter's Performance on a Stanardized Math
Test
Mother's Performance on a Stanardized Math
Test
Father's Performance on a Stanardized Math
Test
84
90
72
65
70
85
91
86
81
75
82
83
81
84
84
79
93
72
83
72
70
92
90
88
61
74
68
73
60
82
85
83
72
90
93
94
54
64
69
70
78
62
Daughter -Mother Correlation:
Instructions: Indicate the correlation between
daughters and mothers' scores on the standardized math 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...

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...

TestScore
53
53
56
56
56
58
58
58
59
59
59
60
60
62
63
63
63
64
65
65
66
67
67
67
67
68
69
69
69
69
71
71
72
72
72
72
73
73
73
73
73
74
75
75
75
76
76
76
76
77
77
77
77
77
78
78
78
79
79
79
79
80
80
80
80
80
80
81
81
81
82
82
83
83
83
83
84
84
84...

Find the mean, median, and mode of the data set. Round it to the
nearest set.
test scores on a math exam:
70, 97, 91, 70, 89, 88, 91, 94, 71, 67, 84, 82, 94, 78, 67, 66,
67, 86, 73, 71, 86, 80

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...

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