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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 = 16

Explanation / 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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