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# Assuming normality and independence, which of the following distributions is used for a comparison of one mean when the sample siz

INSTRUCTIONS TO CANDIDATES
###### ANSWER ALL QUESTIONS

Multiple Choice 2 points each. Note that if your answer due to rounding errors is very close to one of the choices you should select that choice.

1. Assuming normality and independence, which of the following distributions is used for a comparison of one mean when the sample size is 31 and the pop. variance is unknown?

a. t

b. Z

c. Either a or b

d. None of the above

2. Which of the following would encompasses a “concern” about the suitability of a product.

a. Ho

b. Ha

c. Either a or b

d. None of the above

3. Which of the following distributions is used for a comparison of one mean when the sample size is 22 and the pop. variance is unknown?

a. t

b. Z

c. Either a or b

d. None of the above

4. Which of the following distributions is used for a comparison of one mean when the sample size is 24 and the pop. variance is known?

a. t

b. Z

c. Either a or b

d. None of the above

5. Which distribution is used to compare two different sample variances to each other?

a. F

b. t

c. Chi-squared. Z 6. Which distribution is used to test a sample variance to a known population variance?

a. t

b. Chi-square

c. F

d. None of the above

7. If the test statistic is greater than the negative critical value of a two sided test, you.

a. Cannot reject the Ho

b. Reject the Ho

c. Cannot decide from the given information

d. None of the above

8. Assuming independence and normality, to compare two means with n1=25 and n2=35, you would need to use which test.

a. Independent t or Smith-Satterwaithe test

b. Non-parametric test

c. Paired t test

d. None of the above

9. If the test statistic is less than the negative critical value of a two sided test, you.

a. Cannot reject the Ho

b. Reject the Ho

c. Cannot decide from the given information

d. None of the above

10. Mistakenly shipping defective product to a customer means that you have:

a. Committed a type 1 error

b. Committed a type 2 error

c. Made the correct decision

d. None of the above

11. Reporting a false positive on an engineering job interview drug test means the testing facility has?

a. Committed a type 1 error

b. Committed a type 2 error

c. Made the correct decision

d. None of the above

12. As related in class, a soldier took a drug test which indicated that he was?

a. Positive for meth

b. Positive for heroin

c. Positive for alcohol

d. Pregnant

13. Firing an engineer under your supervision for failing a drug test means somebody.

a. Committed a type 1 error

b. Committed a type 2 error

c. Made the correct decision

d. Either a or c

14. A statistical test that involves a “before and after” focus with 40 different subjects has how many degrees of freedom.

a. 19

b. 20

c. 38

d. 39

15. Assuming normality and independence, if n1 or n2 or both are <30, if you have just rejected the Ho in an F test, the next test you are likely to perform is a:

a. independent t test

b. chi-squared test

c. Smith-Satterthwaite test

d. paired t-test

16. Not having a line underneath a set of adjacent means in a Duncan Multiple Ranges test signifies:

a. There is a statistically significant difference

b. There is no statistically significant difference

c. Further information is required to answer

d. None of the above

17. A two sided single mean hypotheses test would have which of the following alternate hypotheses? (< > means not equal)

a. u = > 500

b.   u < = 500

c. u < > 500

d. u = 500

18. A test of means involving two scales and a single set of samples to be weighed on both scales would most likely use what test?

a. Independent t

b. Smith-Satterwaithe

c. Paired t

d. F test

19. If either or both of your data groups for are non-normal from a goodness of fit test, the next test that you would perform is:

a. F test

b. independent t test

c. Smith-satterwaithe test

d. non-parametric u test

20. Assuming normality and independence, if n1 or n2 or both are <30 and if you cannot reject the Ho in an F test, the next test you are likely to perform is a:

a. independent t test

b. chi-squared test

c. Smith-Satterthwaite test

d. paired t-test

Multiple Choice 4 pts each.

21. For an equiprobable chi-squared goodness of fit test with an HO of normally distributed with the same parameters as the sample for 31 obs., you would have how many degrees of freedom.

a. 2

b. 3

c. 4

d. none of the above

22. If you had an equiprobable chi-squared goodness of fit test with an HO of uniformally distributed with a theoretical min of 2.34 and a max of 4.67 and you had 4 cells, what would be the critical value at alpha=0.05

a. 5.991+

b. 7.815

c. 9.488

d. 11.070

23. If your test from the above problem yielded the following data, you would?

24. Assuming normality, to determine which comparison of means test to use, you must first run an F test. For this test the Ho: is the variances are the same. The Ha: is the variances are not the same. At an alpha level of 0.10 what is your decision?

a. Cannot reject Ho

b. Reject Ho

c. I need to retake this course

d. Cannot determine from the above information

25. For the appropriate comparison of means test, calculate the approximate test statistic and determine if you cannot reject or reject the Ho at a 0.05 level assuming normality, independence, and = variance.

a. Cannot reject Ho

b. Reject Ho

c. I need to retake this course

d. None of the above

26. If a company claims that its product, product 1 has at least 50 more operational cycles on the average than a competitors product 2 the most correct Ha would be:

Cell 1 2 3 4

Observed 9 7 5 3 a. Ha: u1-u2 => 0

Expected 5 5 5 5 b. Ha: u1-u2 > 49

c. Ha: u1-u2 < 50

a. Cannot reject Ho

b. Reject Ho

c. Neither

d. Insufficient information to determine

For 24 and 25, you are interested in studying if senior male engineers make more than senior female engineers in annual salaries.

Senior Male Engineers salary in \$ 95,260; 97,854; 98,350; 96,320; 98,340

Senior Female Engineers salary in \$

117,950; 101,890; 107,900; 102,140; 111,920;

101,840

d. Ha: u1-u2 <= 50

For question 27 to 31, the following data represents the number of defects produced before and after quality training in 7 different industrial plants. You would like to see if the training is effective in reducing defects. Before is set 1, after is set 2. Assume normality.

Before 13, 15, 18, 11, 13, 12, 14

After 13, 16, 16, 12, 11, 13, 16

27. What is the null hypotheses? a. u1-u2 = 0

b. uD = 0 or uD>=0

c. uD = 0 or uD<=0

d. uD not =0

28. What is the alternate Hypothesis

a. uD not < 0

b. uD not = 0

c. uD > 0

d. uD < 0

29. What is the critical value for alpha=0.05? a. 2.015

b. 2.132

c. 2.776

d. None of the above

30. Your decision is?

a. Do not reject ho

b. Reject Ho

c. Cannot determine

d. None of the above

31. In English this means that?

a. The training is effective

b. The training is not effective as before

c. The training is less effective as before

d. The training has no effect

32. A sample of 30 beams have an average strength of 1908.8 lbs and s=327.1. What is the 95% confidence interval of the true population mean strength.

a. [1643.8, 1965.8]

b. [1638.9, 1797.8]

c. [1791.7, 2025.8]

d. None of the above

33. A key process indicator for a chemical process has the following values: 123, 106, 114, 128, 113, 109, 120, 102, 111. Assuming normality, what would be approximate 95% confidence interval of mean of this process.

a. [107.59, 120.40]

b. [121.43, 152.39]

c. [143.21, 153.54]

d. None of the above

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