# Hypothesis for difference in the variances: F distribution

A company has two different processes that make credit cards. Suspecting that machine B has a higher variability than machine A the manager orders a test to be run. The following data was collected:

Machine Machine B

Sample size nA= 30 nB=40

Sample Standard Deviation sA= 1.0 sB= 1.7

Select the correct hypothesis to test for the difference in the variances. What is the critical value of the F distribution? Perform the test at the .05 level of significance. What is the observed value of the F distribution? What are your conclusions?

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#### Solution Summary

Hypothesis is tested for the difference in the variances using F distribution.

Correct Hypothesis for Different Variances

1. A company has two different processes that make credit cards. Suspecting that machine B has a higher variability than machine A the manager orders a test to be run. The following data was collected:

Machine A Machine B

Sample size nA= 30 nB=40

Sample Standard Deviation sA= 1.0 sB= 1.7

a. Select the correct hypothesis to test for the difference in the variances.

1. 2.

3. 4.

b. What is the critical value of the F distribution?

c. Perform the test at the .05 level of significance. What is the observed value of the F distribution?

d. What are your conclusions?

2. The null hypothesis and the alternate are:

H0: The cell categories are equal

H1: The cell categories are not equal

Category Observed

A 10

B 20

C 30

Assume a significance level of 5%.

a. What is the critical value of the Chi-square?

b. Compute the observed value of Chi-square.

c. What is your decision regarding H0?

3. Complete the ANOVA summary table shown here.

Source of Variation Sum of Squares Degrees of freedom Mean Square F observed

Between Treatments

150.2

9

Error (Within Treatments)

200.7

Sums of Squares of Total

39

a. How many treatments are there?

b. What is the total sample size?

c. Is there a significant difference at the 5% Level of significance? Would I accept or reject the null Hypothesis. i.e. what is the critical value of the test statistic?