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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

https://brainmass.com/statistics/chi-squared-test/chi-square-test-independence-confidence-interval-6383

#### Solution Preview

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 ...

#### Solution Summary

Uses Chi square test for independence to test the hypothesis that course grade and number of modules completed are dependent, and calculates confidence interval of standard deviation and variance for a set of data.

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