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# Chi square test of independence, Confidence Interval

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Problem 23: In one part of a test developed by a psychologist, the test subject is asked to form a word by unscrambling the letters "ciiatttsss". Given below are times (in seconds) required by 15 randomly selected persons to unscramble the letters. Construct a 95% confidence interval for standard deviation. Assume the population is approximately normal.

Times (in seconds)
68.7
27.4
26
60.5
34.6
61.1
68.6
48.4
43.6
39.5
85.3
26.3
43.4
83.7
68.9

Problem 24: Doing the "Statistics Modules" seems to help statistics students on their exams. Students in several statistics class are classified by grade in the course and by how many modules they completed. There wer 18 possible modules. The results are listed in the following table.

Grade in course 16 or more 9 to 15 8 or less
A 25 9 3
B 18 11 6
C 5 14 12
D or F 2 10 14

Does the data suggest that course grade and number of modules completed are dependent? Use an alpha=0.05 level of significance

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23 In one part of a test developed by a psychologist, the test subject is asked to form a word by unscrambling the letters "ciiatttsss". Given below are times (in seconds) required by 15 randomly selected persons to unscramble the letters. Construct a 95% confidence interval for standard deviation. Assume the population is approximately normal.

Times (in seconds)
68.7
27.4
26
60.5
34.6
61.1
68.6
48.4
43.6
39.5
85.3
26.3
43.4
83.7
68.9

First we calculate variance and standard deviation of the data
Score (Score-mean)^2
68.7 265.69000
27.4 625.00000
26 696.96000
60.5 65.61000
34.6 316.84000
61.1 75.69000
68.6 262.44000
48.4 16.00000
43.6 77.44000
39.5 166.41000
85.3 1082.41000
26.3 681.21000
43.4 81.00000
83.7 979.69000
68.9 272.25000
786.00 5664.64000
n= 15
mean= 52.4 =786/15
Variance=s 2 404.6171429 =5664.64/14
standard deviation= 20.1151 =square root of 404.617143

Find Chi square values for 95% confidence interval
Degrees of fredom=15-1=14
chi square vlaues
X upper ^2 = 26.11894805
X lower ^2 = 5.628726168
Variance Standard deviation=square root of Variance
s L 2 = (n-1) s ^2 / X upper ^2 = 216.87857 14.7268
s U 2 = (n-1) s ^2 / X lower ^2 = 1006.38045 31.7235

95% confidence interval
Lower limit of standard deviation 31.7235
Upper limit of standard deviation 14.7268

Problem 24

Doing the "Statistics Modules" seems to help statistics students on their exams. Students in several statistics class are classified by grade in the course and by how many modules they completed. There wer 18 possible modules. The results are listed in the following table.

Grade in course 16 or more 9 to 15 8 or less
A 25 9 3
B 18 11 6
C 5 14 12
D or F 2 10 14

Does the data suggest that course grade and number of modules completed are dependent? Use an alpha=0.05 level of significance

Null Hypothesis: Course grade and number of modules completed are independent
Alternative Hypothesis: Course grade and number of modules completed are dependent

Theoretical=Row total X column total/n
Thus for Grade A and >16 theoretical=37*50/129= 14.3411
and so on

No of modules completed

>16 9-15 <8
Grade in course Actual Theoretical Actual Theoretical Actual Theoretical Row total

A 25 14.3411 9 12.6202 3 10.0388 37

B 18 13.5659 11 11.938 6 9.4961 35

C 5 12.0155 14 10.5736 12 8.4109 31

D or F 2 10.0775 10 8.8682 14 7.0543 26
129

Column total 50 44 35

Chi square value= summation of (fo-fe)^2/fe= 36.9017

fo fe (fo-fe)^2/fe
25 14.3411 7.92214

18 13.5659 1.44931

5 12.0155 4.09615

2 10.0775 6.47442

9 12.6202 1.03848

11 11.938 0.0737

14 10.5736 1.11033

10 8.8682 0.14445

3 10.0388 4.93532

6 9.4961 1.28713

12 8.4109 1.53154

14 7.0543 6.83877
36.9017

No of degrees of freedom= (No of rows-1)*(No of columns-1)=(4-1)*(3-1)=6

alpha (a) = 0.05

Chi square value= 12.5916 from the tables

Accptance region for null hypothesis is upto 12.5916

Since Chi square value computed in this case= 36.9017
which lies to the right of acceptance region of 12.5916
Reject Null Hypothesis
Course grade and number of modules completed are dependent

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

© BrainMass Inc. brainmass.com October 2, 2022, 5:39 pm ad1c9bdddf>
https://brainmass.com/statistics/chi-squared-test/chi-square-test-independence-confidence-interval-6383