What is the critical value of the f distribution

Question

Assignment:

Q1. 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. H0:σ²_A = σ²_B             H1:σ²_A ≠ σ²_B

2. H0: σ²_A ≥ σ²_B            H1:σ²_A < σ²_B

3. H0:σ²_A ≠ σ²_B              H1:σ²_A = σ²_B

4. H0:  σ²_A ≤ σ²_B            H1:σ²_A  >σ²_B

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? Select 1 or 2.

1. B has a higher variability than machine A

2. B does not have a higher variability than machine A

Q2. 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?

1. The cell categories are equal

2. The cell categories are not equal

Q3. 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?

d. Select one of the following.

1. There is a significant difference between the treatments

2. There is no significant difference between the treatments

e. Suppose x_‾1=14.9 and x_‾2=18.5 we are testing to see if there a statistical difference between treatment 1 and treatment 2 using a 5% significance level? Assume equal sample sizes for each treatment.

1. What is the confidence interval for x_‾1 - x‾2

2. Is there a statistical difference between treatment 1 and 2? Yes, or No?