A sample of 18 male students was asked how much they spent on textbooks this sem
ID: 3434759 • Letter: A
Question
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.Explanation / Answer
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