Reference no: EM132314923
Basic Statistics Lab Assignment -
Note:
1. All questions are compulsory.
2. Solve the following questions in MS Excel.
3. Take the screenshots of the final output/spreadsheet.
4. Paste all screenshots in the assignments booklets with all necessary hypotheses, interpretation, etc.
Q1. A researcher conducted a stimulus reaction experiment on 50 subjects to a threatening stimulus and 50 subjects to a nonthreatening stimulus. The reaction times of all 100 students to the nearest tenth of a second-were recorded as follows:
Reaction Times of Students
|
Nonthreatening Stimulus
|
|
2.4
|
2.2
|
2.7
|
2.5
|
2.4
|
2.6
|
2.5
|
2.6
|
2.5
|
2.5
|
|
2.4
|
2.4
|
2.2
|
2.3
|
2.6
|
2.4
|
2.6
|
2.8
|
2.5
|
2.4
|
|
2.6
|
2.5
|
2.6
|
2.3
|
2.1
|
2.4
|
2.4
|
2.7
|
2.5
|
2.3
|
|
2.4
|
2.6
|
2
|
2.5
|
2.7
|
2.4
|
2.4
|
2.4
|
2.6
|
3
|
|
2.4
|
2.4
|
2.3
|
2.3
|
2.6
|
2.7
|
2.2
|
2.1
|
2.1
|
2.2
|
|
Threatening Stimulus
|
|
2.2
|
2.1
|
1.8
|
2.5
|
1.7
|
1.9
|
2
|
2.2
|
1.9
|
1.8
|
|
1.8
|
2.4
|
1.9
|
2.2
|
1.8
|
2.1
|
2.1
|
2.1
|
1.8
|
2.3
|
|
2.3
|
2.1
|
2
|
2.9
|
2
|
2
|
2.2
|
2.1
|
2.3
|
2.3
|
|
1.9
|
2.2
|
2
|
2.3
|
1.7
|
1.9
|
2
|
1.9
|
2
|
1.9
|
|
1.7
|
2.1
|
1.7
|
2.1
|
2.1
|
2.2
|
2
|
2.1
|
2.1
|
2.1
|
Answer the following:
i) Which stimulus has more average reaction?
ii) Which stimulus showed more consistent result?
iii) Compute suitable width of the class intervals for both types of stimulus and construct the continuous frequency distribution for both.
iv) Also, construct the histogram for both types of stimulus and interpret the results.
Q2. The marks (out of 100) given to the twenty candidates in a job interview on the basis of various parameters of the selection, are presented in the table given below:
|
S. No.
|
Examiner I
|
Examiner II
|
Examiner III
|
|
1
|
58
|
82
|
60
|
|
2
|
53
|
77
|
59
|
|
3
|
40
|
76
|
56
|
|
4
|
68
|
91
|
71
|
|
5
|
51
|
89
|
69
|
|
6
|
50
|
79
|
62
|
|
7
|
65
|
98
|
74
|
|
8
|
60
|
92
|
71
|
|
9
|
61
|
85
|
63
|
|
10
|
47
|
77
|
60
|
|
11
|
64
|
93
|
73
|
|
12
|
58
|
96
|
74
|
|
13
|
60
|
100
|
79
|
|
14
|
59
|
89
|
66
|
|
15
|
57
|
93
|
70
|
|
16
|
67
|
89
|
68
|
|
17
|
54
|
71
|
51
|
|
18
|
71
|
100
|
75
|
|
19
|
54
|
71
|
53
|
|
20
|
58
|
91
|
68
|
i) Use the rank correlation coefficient to determine which pair of examiners had the nearest approach in selection of candidates.
ii) Also represent the marks given by three examiners using box plot.
Q3. For the data given in question 1, if the reaction time for both stimulus are normally distributed, then answers the following questions:
i) Are the variances of the distributions of the reaction time for both stimulus equal at 5% level of significance?
ii) Also, check whether the average reaction time for nonthreatening stimulus is more than the threatening stimulus at 5 % level of significance?
Q4. A researcher wanted to compare the mean distance covered by four brands of golf balls struck by various types of clubs. The six golfers (A, B, C, D, E and F) are assigned at random to 36 cells of the square with the restriction that each golfer will hit each brand of ball only once using each type of club. The following design was obtained in which 6 brands of balls are arranged in "columns" and 6types of clubs are in "rows":
|
|
Brand of Ball
|
|
1
|
2
|
3
|
4
|
5
|
6
|
|
Type of Club
|
1
|
A
|
B
|
C
|
D
|
E
|
F
|
|
2
|
B
|
C
|
D
|
E
|
F
|
A
|
|
3
|
C
|
D
|
E
|
F
|
A
|
B
|
|
4
|
D
|
E
|
F
|
A
|
B
|
C
|
|
5
|
E
|
F
|
A
|
B
|
C
|
D
|
|
6
|
F
|
A
|
B
|
C
|
D
|
E
|
The average distance covered by each ball is given as follows:
|
|
Brand of Ball
|
|
1
|
2
|
3
|
4
|
5
|
6
|
|
Type of Club
|
1
|
133
|
139
|
140
|
140
|
145
|
138
|
|
2
|
136
|
141
|
143
|
146
|
139
|
142
|
|
3
|
140
|
138
|
142
|
139
|
139
|
141
|
|
4
|
129
|
132
|
137
|
136
|
140
|
138
|
|
5
|
132
|
144
|
143
|
142
|
142
|
140
|
|
6
|
138
|
140
|
141
|
137
|
141
|
139
|
Assuming that the effect of each golfer, ball and club are normally distributed with approximately equal variances; analyse the design at 1% level of significance. Test whether the effect of the different golfer, ball and club on the distance covered are significant or not. If significant, do the pair-wise comparison between them.
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