A sample of 18 male students was asked how much they spent o

A sample of 18 male students was asked how much they spent on textbooks this semester. The sample variance was s2M = 35.05. A sample of eight female students was asked the same question, and the sample variance was s2F = 18.40. (Data collected by Megan Damron and Spencer Solomon, 2009.) Assume that the amount spent on textbooks is normally distributed for both the populations of male students and of female students. Calculate a 90% confidence interval estimate for sigma2M, the population variance of the amount spent on textbooks by male students. Calculate a 90% con?dence interval estimate for sigma2M, the population variance of the amount spent on textbooks by female students.

Solution

a).Confidence Interval Estimate for the Population Variance

Data

Sample Size

18

Sample Standard Deviation

5.92030405

Confidence Level

90%

Intermediate Calculations

Degrees of Freedom

17

Sum of Squares

595.85

Single Tail Area

0.05

Lower Chi-Square Value

8.6718

Upper Chi-Square Value

27.5871

Results

Interval Lower Limit for Variance

21.5989

Interval Upper Limit for Variance

68.7115

b).

Confidence Interval Estimate for the Population Variance

Data

Sample Size

8

Sample Standard Deviation

4.28952212

Confidence Level

90%

Intermediate Calculations

Degrees of Freedom

7

Sum of Squares

128.8

Single Tail Area

0.05

Lower Chi-Square Value

2.1673

Upper Chi-Square Value

14.0671

Results

Interval Lower Limit for Variance

9.1561

Interval Upper Limit for Variance

59.4274

a).Confidence Interval Estimate for the Population Variance
Data
Sample Size	18
Sample Standard Deviation	5.92030405
Confidence Level	90%
Intermediate Calculations
Degrees of Freedom	17
Sum of Squares	595.85
Single Tail Area	0.05
Lower Chi-Square Value	8.6718
Upper Chi-Square Value	27.5871
Results
Interval Lower Limit for Variance	21.5989
Interval Upper Limit for Variance	68.7115