Data Set 1
Question 1 – Independent sample t-test
𝐻
0
: morning class short answer score = afternoon short answer scores or 𝜇 morning = 𝜇 afternoon
𝐻
1
: morning class short answer score ≠ afternoon short answer scores or 𝜇 morning ≠ 𝜇 afternoon
X1 morning scores: 59,64,65,70,67,58,79
X2 afternoon scores: 40,45,55,55,60,70,60,63 𝑥̅ 𝑥̅ 𝑥̅
1
1
1
=
=
∑𝑥 𝑛
462
7
= 66 𝑥̅ 𝑥̅ 𝑥̅
2
2
2
=
=
∑𝑥 𝑛
448
8
= 56
68
66
64
62
60
58
56
54
52
50
Morning
Class
Afternoon
Class 𝑛
1
= 7 𝑛
2
=8 𝑥̅
1
= 66 𝑥̅
2
= 56
𝑆
2
1
= ∑
𝑆
2
1
= ∑
(𝑥−𝑥̅
1 𝑛
1
−1
)
2
(59−66
1
) 2
+(64−66
1
) 2
+(65−66
1
) 2
+(70−66
1
) 2
+(67−66
1
) 2
+(58−66
1
) 2
+(79−66
1
) 2 𝑛
1
−1
𝑆
2
1
= 50.67
𝑆
2
2
= ∑
(𝑥−𝑥̅
2 𝑛
2
−1
) 2
𝑆
2
2
= ∑
𝑆 2
2
(40−56
2
) 2
+(45−56
2
) 2
+(55−56
2
) 2
+(55−56
2
) 2
+(60−56
2
) 2
+(70−56
2
) 2
+(60−56
2
) 2
+(63−56
2
) 2 𝑛
1
−1
= 93.71
Continued…

𝑆
2 𝑝
=
(𝑛
1
− 1)𝑆
2
1
+ (𝑛
2 𝑛
1
+ 𝑛
2 −2
− 1)𝑆
2
2
𝑆
2 𝑝
=
6𝑥50.67 + 7𝑥93.71
7 + 8 − 2
𝑆 2 𝑝
=
6𝑥50.67 + 7𝑥93.71
7 + 8 − 2
𝑆
2 𝑝
=
655.97
13
𝑆 2 𝑝
= 73.85
𝑡 = 𝑥̅
1
−𝑥̅
2
√ 𝑛1
+ 𝑛2 𝑡 =
66−56
√
73.85
7
+
73.85
8 𝑡 = 2.2484
𝑡 ∗ (13) = 2.2160 < 2.2484
Conclusion:
Reject 𝐻
0
, scores differ between morning and afternoon classes.
Question 2 – Paired Sample t-test
𝐻
0
: short answer score = multiple choice scores or 𝜇 short answer = 𝜇 multiple choice
𝐻
1
: short answer score ≠ multiple choice scores or 𝜇 short answer ≠ 𝜇 multiple choice