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

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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