A comparison of the precisions of two machines developed for extracting juice fr
ID: 3160121 • Letter: A
Question
A comparison of the precisions of two machines developed for extracting juice from oranges is to be made using the following data.
(a) Is there sufficient evidence to indicate that there is a difference in the precision of the two machines at the 5% level of significance? (Round your answers to two decimal places.)
Test statistic: F =
Rejection region: F >
(b) Find a 95% confidence interval for the ratio of the two population variances. (Round your answers to two decimal places.)
_________ to _________
Machine A Machine B s2 = 3.1 ounces2 s2 = 1.6 ounces2 n = 16 n = 16Explanation / Answer
A comparison of the precisions of two machines developed for extracting juice from oranges is to be made using the following data.
(a) Is there sufficient evidence to indicate that there is a difference in the precision of the two machines at the 5% level of significance? (Round your answers to two decimal places.)
Machine A
Machine B
n = 16
n = 16
Test statistic: F = 1.94
Rejection region: F >2.86
The null hypothesis is not rejected.
There is not sufficient evidence to indicate that there is a difference in the precision of the two machines.
F Test for Differences in Two Variances
Data
Level of Significance
0.05
Larger-Variance Sample
Sample Size
16
Sample Variance
3.1
Smaller-Variance Sample
Sample Size
16
Sample Variance
1.6
Intermediate Calculations
F Test Statistic
1.9375
Population 1 Sample Degrees of Freedom
15
Population 2 Sample Degrees of Freedom
15
Two-Tail Test
Upper Critical Value
2.8621
p-Value
0.2118
Do not reject the null hypothesis
(b) Find a 95% confidence interval for the ratio of the two population variances. (Round your answers to two decimal places.)
0.68 to5.55
95% Confidence Intervals
CI for
CI for StDev Variance
Method Ratio Ratio
F (0.823, 2.355) (0.677, 5.545)
Machine A
Machine B
n = 16
n = 16
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