Construct a 90% confidence interval for the ratio between the variance of lifeti
ID: 3132969 • Letter: C
Question
Construct a 90% confidence interval for the ratio between the variance of lifetime of group A and the variance of lifetime of group B. Interpret your confidence interval. What is the observed ratio of variances?
We would like to see if the variance of lifetime of group A is significantly different from that of lifetime of group B at level of 0.1. Perform a two variances Hypothesis Test. What is the test statistic and p-value? What is your decision (can we reject the null hypothesis)? Does your decision agree with your confidence interval above?
brand lifetime group 1 1.8 A 1 5 A 1 1 A 2 4.2 A 2 5.4 A 2 4.2 A 3 8.6 A 3 4.6 A 3 4.2 A 4 7 A 4 5 A 4 9 A 5 4.2 B 5 7.8 B 5 6.6 B 6 4.2 B 6 4.2 B 6 5.4 B 7 7.8 B 7 7 B 7 9.8 B 8 9 B 8 7.4 B 8 5.8 BExplanation / Answer
Construct a 90% confidence interval for the ratio between the variance of lifetime of group A and the variance of lifetime of group B. Interpret your confidence interval. What is the observed ratio of variances?
We would like to see if the variance of lifetime of group A is significantly different from that of lifetime of group B at level of 0.1. Perform a two variances Hypothesis Test. What is the test statistic and p-value? What is your decision (can we reject the null hypothesis)? Does your decision agree with your confidence interval above?
Test and CI for Two Variances: A, B
Method
Statistics
90% CI for
Variable N StDev Variance StDevs
A 12 2.363 5.585 (1.726, 3.750)
B 12 1.884 3.549 (1.479, 2.781)
Ratio of standard deviations = 1.255
Ratio of variances = 1.574
Table values of F(11,11) =(0.355,2.818)
90% Confidence Intervals=(1.255/2.818, 1.255/0.355)
=(0.445, 3.535)
Null hypothesis (A) / (B) = 1
Alternative hypothesis (A) / (B) 1
Significance level = 0.1
F Test for Differences in Two Variances
Data
Level of Significance
0.1
Larger-Variance Sample
Sample Size
12
Sample Variance
5.5855
Smaller-Variance Sample
Sample Size
12
Sample Variance
3.5491
Intermediate Calculations
F Test Statistic
1.5738
Population 1 Sample Degrees of Freedom
11
Population 2 Sample Degrees of Freedom
11
Two-Tail Test
Upper Critical Value
2.8179
p-Value
0.4641
Do not reject the null hypothesis
Test statistic = 1.57and p-value=0.4641
Do not reject the null hypothesis.
There is not sufficient evidence to conclude that the variance of of is significantly different from that of of at level of 0.1.
This decision agree with the above confidence interval because the 90% CI contains the value 1.
F Test for Differences in Two Variances
Data
Level of Significance
0.1
Larger-Variance Sample
Sample Size
12
Sample Variance
5.5855
Smaller-Variance Sample
Sample Size
12
Sample Variance
3.5491
Intermediate Calculations
F Test Statistic
1.5738
Population 1 Sample Degrees of Freedom
11
Population 2 Sample Degrees of Freedom
11
Two-Tail Test
Upper Critical Value
2.8179
p-Value
0.4641
Do not reject the null hypothesis