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.
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 | 76 | 79 |
79829 | 79 | 75 |
62759 | 83 | 66 |
60967 | 84 | 83 |
82719 | 76 | 74 |
59420 | 82 | 70 |
69717 | 85 | 82 |
67553 | 85 | 82 |
67762 | 91 | 75 |
60851 | 72 | 78 |
81587 | 86 | 99 |
82947 | 70 | 57 |
62831 | 91 | 91 |
79864 | 82 | 78 |
67627 | 73 | 87 |
70270 | 96 | 93 |
54637 | 64 | 89 |
65582 | 74 | 81 |
64976 | 88 | 84 |
66027 | 88 | 63 |
77528 | 60 | 78 |
68129 | 73 | 66 |
56098 | 83 | 84 |
75695 | 85 | 85 |
66311 | 82 | 85 |
72678 | 79 | 84 |
80248 | 75 | 59 |
63594 | 82 | 62 |
53448 | 88 | 91 |
53454 | 86 | 83 |
59507 | 83 | 80 |
57192 | 70 | 76 |
Using Excel, go to Data, select Data Analysis, choose t-Test: Two-Sample Assuming Unequal Variances.
Mid | Final | |
Mean | 81.825 | 78 |
Variance | 69.994 | 101.641 |
Observations | 40 | 40 |
Hypothesized Mean Difference | 0 | |
df | 75 | |
t Stat | 1.847 | |
P(T<=t) one-tail | 0.0344 | |
t Critical one-tail | 1.665 | |
P(T<=t) two-tail | 0.069 | |
t Critical two-tail | 1.992 |
H_{0}: μ_{1} = μ_{2}
H_{1}: μ_{1} > μ_{2}
p-value = 0.034
Since p-value is less than 0.05, we reject the null hypothesis and conclude that μ_{1} > μ_{2}.
So, students score lower on their final exxam than mid exxam.
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