Question

In: Statistics and Probability

QUESTION 13 Psychology Final Question 1 A professor teaches two sections of a Psychology class. The...

QUESTION 13

Psychology Final Question 1

A professor teaches two sections of a Psychology class. The placement of the enrolled students in the two sections is done randomly. In Section 1, students are required to participate in weekly study groups. In Section 2, there is no such requirement. The data file FINAL.MWX (for Minitab 19) or FINAL.MTW (for Minitab 18) contains the final exam scores of students in these two sections. Let µ1 and µ2 denote the average score in Section 1 and Section 2, respectively.

Find a 90% confidence interval for µ2-µ1.

a. (-6.38, -0.82)

b. (9.43, 14.52)

c. (-14.46, -9.49)

d. (-5.61, -0.05)

e. (1.27, 7.89)

Class 1 Class 2

50 74

73 79

54 68

90 62

63 55

70 76

70 66

47 81

81 64

93 88

69 97

62 72

38 78

65 81

82 77

48 81

38 85

57 78

65 79

40 62

62 95

44 52

60 100

67 78

63 82

85 67

71 80

69 70

95 72

85 83

90 73

60 68

49 90

55 70

35 76

82 81

82 86

85 63

51 65

78 77

42 82

40 54

82 85

82 59

60 97

76 81

79 76

69 71

90 78

39 85

41 80

42 75

59 48

47 66

61 75

59 94

38 62

44 92

48 86

66 68

71 58

64 95

84 61

60 72

77 83

63 87

62 94

42 94

60 59

73 53

38 67

52 68

40 64

42 65

86 74

83 91

94 68

73 78

42 86

60 74

65 68

57 82

94 62

44 83

39 62

76 78

37 77

62 72

51 61

40 60

55 65

74 69

35 82

90 45

78 70

44 89

66 73

78 92

84 78

52 71

63 85

62 56

88 91

80 53

88 91

65 67

91 87

66 49

36 64

86 79

82 73

73 66

38 66

42 80

39 92

73 80

73 87

93 61

75 83

51 71

47 86

75 73

57 70

66 76

41 56

40 71

59 83

81 84

56 92

41 69

81 88

80 72

49 62

69 75

79 57

69 78

62 83

93 73

76 80

36 84

95 90

80 99

66 78

74 94

68 74

67 64

79 97

37 69

66 89

52 87

81 79

42 57

73 75

55 79

46 88

81 85

92 64

84 66

76 84

36 75

65 97

35 76

61 62

38 82

48 90

44 52

64 81

78 43

61 88

71 67

49 77

65 83

72 85

67 58

40 86

56

71

75

80

94

74

87

89

70

73

66

90

84

87

76

94

61

69

78

51

76

87

62

78

Expert Solution

since, n>30 in both the samples, we will use a t-test for two independent sample means.

since the Population sample deviation is not available and the samples are independent.

the data is given as

class 1	class 2
50	74
73	79
54	68
90	62
63	55
70	76
70	66
47	81
81	64
93	88
69	97
62	72
38	78
65	81
82	77
48	81
38	85
57	78
65	79
40	62
62	95
44	52
60	100
67	78
63	82
85	67
71	80
69	70
95	72
85	83
90	73
60	68
49	90
55	70
35	76
82	81
82	86
85	63
51	65
78	77
42	82
40	54
82	85
82	59
60	97
76	81
79	76
69	71
90	78
39	85
41	80
42	75
59	48
47	66
61	75
59	94
38	62
44	92
48	86
66	68
71	58
64	95
84	61
60	72
77	83
63	87
62	94
42	94
60	59
73	53
38	67
52	68
40	64
42	65
86	74
83	91
94	68
73	78
42	86
60	74
65	68
57	82
94	62
44	83
39	62
76	78
37	77
62	72
51	61
40	60
55	65
74	69
35	82
90	45
78	70
44	89
66	73
78	92
84	78
52	71
63	85
62	56
88	91
80	53
88	91
65	67
91	87
66	49
36	64
86	79
82	73
73	66
38	66
42	80
39	92
73	80
73	87
93	61
75	83
51	71
47	86
75	73
57	70
66	76
41	56
40	71
59	83
81	84
56	92
41	69
81	88
80	72
49	62
69	75
79	57
69	78
62	83
93	73
76	80
36	84
95	90
80	99
66	78
74	94
68	74
67	64
79	97
37	69
66	89
52	87
81	79
42	57
73	75
55	79
46	88
81	85
92	64
84	66
76	84
36	75
65	97
35	76
61	62
38	82
48	90
44	52
64	81
78	43
61	88
71	67
49	77
65	83
72	85
67	58
40	86
	56
	71
	75
	80
	94
	74
	87
	89
	70
	73
	66
	66
	90
	84
	87
	76
	94
	61
	69
	78
	51
	76
	87
	62
	78

the 90% confidence Interval for is given by

where s_{p is}

from the Descriptive summary, we get,

class 1		class 2

Mean	63.44571429	Mean	75.41
Standard Error	1.287902972	Standard Error	0.84619129
Median	65	Median	76
Mode	73	Mode	78
Standard Deviation	17.03735488	Standard Deviation	11.96695198
Sample Variance	290.2714614	Sample Variance	143.2079397
Kurtosis	-1.099133088	Kurtosis	-0.444786654
Skewness	-0.026939637	Skewness	-0.255490363
Range	60	Range	57
Minimum	35	Minimum	43
Maximum	95	Maximum	100
Sum	11103	Sum	15082
Count	175	Count	200
Confidence Level(90.0%)	2.129751074	Confidence Level(90.0%)	1.398370662

let X be the values of class1 and Y be the Value of class 2.

alpha = 0.1

therefore, zalpha/2 = 1.645.

63.44571429

75.41

= 290.2714614

= 143.20

n₁ = 175,

n₂ = 200

s_p² = 211.8112984

t_373,0.05= 1.648949026

therefore, the 90% confidence Interval for is (-14.44835, -9.4802181).

therefore, the 90% Confidence Interval for is ( 9.4802181 , 14.44835).

which is close to option b

We were unable to transcribe this image

(-1) = zarnavniet (Z - 4)^=a/2

We were unable to transcribe this image

orchestra answered 2 years ago

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