(i) J(i) K(i) L(i) M(i) 1 101.20 85.10 97.72 96.55 2 98.62 94.31 92.66 131.23 3
ID: 3365236 • Letter: #
Question
(i) J(i) K(i) L(i) M(i) 1 101.20 85.10 97.72 96.55 2 98.62 94.31 92.66 131.23 3 103.57 89.56 105.03 104.00 4 107.93 93.59 110.97 98.29 5 101.46 92.08 105.72 102.21 6 101.88 82.85 100.44 104.97 7 96.15 86.22 107.98 113.09 8 109.46 88.47 94.30 112.72 9 94.52 93.11 103.36 105.55 10 106.85 81.05 97.60 108.49 11 102.80 91.52 96.34 92.25 12 94.50 82.90 108.85 125.44 Question 8. Now we want to test whether the variances of the populations under study conform to the claimed value of 2-25. This is done using a 2 test. a) How many degrees of freedom are appropriate for this test? b) Develop two-sided confidence interval for 2 c) Determine whether the samples support the claim that 2-25 for each of the data sets.Explanation / Answer
Result:
a). df= 12-1=11
b).
Two-Tail chi square Test
Lower Critical Value
3.8157
Upper Critical Value
21.9200
Descriptive statistics
J(i)
K(i)
L(i)
M(i)
count
12
12
12
12
mean
101.5783
88.3967
101.7475
107.8992
sample standard deviation
4.9918
4.6651
6.0747
11.4027
sample variance
24.9185
21.7630
36.9019
130.0225
data set J
Chi-Square Test of Variance
Data
Null Hypothesis s^2=
25
Level of Significance
0.05
Sample Size
12
Sample Standard Deviation
4.9918
Intermediate Calculations
Degrees of Freedom
11
Half Area
0.025
Chi-Square Statistic
10.9639
Two-Tail Test
Lower Critical Value
3.8157
Upper Critical Value
21.9200
p-Value
0.4463
Do not reject the null hypothesis
Do not reject the claim.
Data set K
Chi-Square Test of Variance
Data
Null Hypothesis s^2=
25
Level of Significance
0.05
Sample Size
12
Sample Standard Deviation
4.6651
Intermediate Calculations
Degrees of Freedom
11
Half Area
0.025
Chi-Square Statistic
9.5758
Two-Tail Test
Lower Critical Value
3.8157
Upper Critical Value
21.9200
p-Value
0.4311
Do not reject the null hypothesis
Do not reject the claim.
Data set L
Chi-Square Test of Variance
Data
Null Hypothesis s^2=
25
Level of Significance
0.05
Sample Size
12
Sample Standard Deviation
6.0747
Intermediate Calculations
Degrees of Freedom
11
Half Area
0.025
Chi-Square Statistic
16.2369
Two-Tail Test
Lower Critical Value
3.8157
Upper Critical Value
21.9200
p-Value
0.1326
Do not reject the null hypothesis
Do not reject the claim.
Data set M
Chi-Square Test of Variance
Data
Null Hypothesis s^2=
25
Level of Significance
0.05
Sample Size
12
Sample Standard Deviation
11.4027
Intermediate Calculations
Degrees of Freedom
11
Half Area
0.025
Chi-Square Statistic
57.2095
Two-Tail Test
Lower Critical Value
3.8157
Upper Critical Value
21.9200
p-Value
0.0000
Reject the null hypothesis
Reject the claim.
Two-Tail chi square Test
Lower Critical Value
3.8157
Upper Critical Value
21.9200
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