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(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