# Chi square test of independence, Confidence Interval

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

#### Solution Preview

Please see attached file for answers.

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.