# Statistics: Frequency, Chi-Square, Mean Square, and Error

Use the following information to answer questions: A manufacturer of automobile transmissions uses three different processes. The management ordered a study of the production costs to see if there is a difference among the three processes. A summary of the findings is shown below.

Process 1 Process 2 Process 3 Total

Process Total ($100's) 137 108 107 352

Sample Size 10 10 10 30

Sum of Squares 1893 1188 1175 4256

1. What is the sum of squares for the treatment?

a. 67.80

b. 58.07

c. 149.34

d. 23.47

2. What is the sum of squares of the error?

a- 67.80

b- 58.07

c- 149.34

d- 23.47

3. What is the critical value of F at the 5% level of significance?

a- 19.45

b- 3.00

c- 3.35

d- 3.39

4. What is the degree of freedom for the numerator of the F ratio?

a. 2

b. 3

c. 10

d. 27

5. What is the degree of freedom for the denominator?

a. 3

b. 10

c. 27

d. 30

6. What is the mean square for the treatments?

a. 2.511

b. 2.151

c. 33.9

d. 29.035

7. What is the mean square for error?

a. 2.511

b. 2.151

c. 33.9

d. 29.035

8. What is the calculated F?

a. 0.086

b. 1.168

c. 11.56

d. 13.50

Use the following information to answer questions:

The personnel manager is concerned about absenteeism. She decides to sample the records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis to be tested is:

Absenteeism is distributed evenly throughout the week.

The 0.01 level is to be used. The sample results are:

Day of week Number Absent

Monday 12

Tuesday 9

Wednesday 11

Thursday 10

Friday 9

Saturday 9

9. What kind of frequencies are the numbers 12, 9, 11, 10, 9, and 9 called?

a. Acceptance

b. Critical value

c. Expected

d. Observed

10. How many degrees of freedom are there?

a. 0

b. 3

c. 4

d. 5

11. What is the expected frequency?

a. 9

b. 10

c. 11

d. 12

12. What is the calculated value of chi-square?

a. 1.0

b. 0.5

c. 0.8

d. 8.0

https://brainmass.com/statistics/hypothesis-testing/statistics-237488

#### Solution Summary

This solution identifies the correct answer for statistical questions and justifies why with calculations. It touches on various topics such as expect frequency, chi-square, mean square, sum of squares and errors.

Hypothesis Testing: Test Statistics T Test

See attached files for tables.

6) In order to test the effects of replacing the bearings on different machines, ten different machines are chose. The number of parts produced in the hour before replacing the bearings and the number of parts produced in the hour after replacing the bearings is recorded. (Chart is on attachment).

A. Write the hypotheses that would be used to test the hypothesis that the production before replacing the bearings was greater than after replacing them.

B. Give the value of the test statistic and the p-value of the test:

t= p-value=

C. What is the decision?

D. Determine the 90% confidence interval for the difference in production per hour

E. What is the point estimate for the estimate for the difference in production from before and after the bearings are replaced?

F. What would you report to management as the effects of replacing the bearings?

7 a. How many randomly selected name brand computers would you need to estimate the mean price within +-$140 with a 90% confidence, if prior knowledge tells you that (symbol on attachment) $1,630? Show your work.

B. Name two ways you could reduce the required size of this sample.

8. In an effort to determine if level of education is a factor in the rate of layoff's the following data was gathered. Use a 0.05 level of significance to test independence.

(Chart on attachment)

A. State the hypotheses being tested.

B. The name of the test statistic is with degrees of freedom

C. Give the computed value of the test statistic.

D. What is the P-value of the test?

E. What is the critical value of the test statistic?

F. State and explain the decision.