Question

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	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

Answer 1

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

H₀: μ₁ = μ₂

H₁: μ₁ > μ₂

p-value = 0.034

Since p-value is less than 0.05, we reject the null hypothesis and conclude that μ₁ > μ₂.

So, students score lower on their final exxam than mid exxam.