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SOSC 2225 Statistics Final Ch 7-9

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SOSC 2225 Statististics Final      Name______________________

Chapters 7-9

1. The goal of estimation procedures is to infer ___________ from ____________.

a. intervals, estimates

b. bias, efficiency

c. statistics, parameters

d. parameters, statistics

2. Public opinion polls and election projections are examples of

a. estimation procedures

b. hypothesis testing

c. non-statistical research methods

d. blatant misuse of statistical procedures

3. Between 70% and 80% of the people who do the family grocery shopping are women. This is

a. not a finding which can be generalized

b. a point estimate

c. an interval estimate

d. sexism at its most offensive

4. From a random sample of 300 state university students, you found that the average number of hours of study time each week is 30 with a standard deviation of 5. A point estimate of the average study time for all state university students would be

a. 5

b. 30

c. 300

d. 15 1 standard deviation

5. Two sample statistics are unbiased estimators. They are

a. means and proportions

b. means and standard deviations

c. medians and modes

d. proportions and percentages

6. The probability that a sample mean is within 1 Z of the population mean is about

a. .34

b. .68

c. .95

d. .99

7. In ________ of the cases, the mean of a sample selected by EPSEM will be more than 3 Z's from the population mean.

a. less than 1%

b. more than 5%

c. more than 90%

d. more than 99%

8. The efficiency of a sample estimator is essentially a matter of

a. accuracy

b. validity

c. centrality

d. dispersion

9. The sizes of four samples vary as follows:

Sample A, N = 100

Sample B, N = 76

Sample C, N =1000

Sample D, N = 150

Which sample will produce the most efficient estimate?

a. Sample A

b. Sample B

c. Sample C

d. Sample D

10. The efficiency of any estimator can be improved by

a. increasing the sample size

b. decreasing the sample size

c. making the sample representative

d. changing the sample

11. The more efficient the estimate, the more the sampling distribution

a. is evenly spread from the mean to 2 standard deviations

b. becomes flatter

c. clusters to the right of the mean

d. is clustered around the mean

12. The probability that an interval estimate does not include the population value is called

a. the margin

b. alpha

c. an error

d. the odds

13. An alpha level of 0.05 is the same as a confidence level of

a. 99.5%

b. 95%

c. 90.5%

d. 90%

14. To decrease the probability that a confidence interval will NOT include the population parameter

a. lower the alpha level

b. raise the alpha level

c. increase the bias of the sample statistic

d. set efficiency to zero

15. We have used an alpha of 0.01 to estimate the average hours of television viewing for residents in a retirement home. What is the chance that our interval estimate does not contain the true population mean?

a.. 99%

b. 10%

c. 1%

d. 1/10 of 1%

16. The average weight of a sample of women who attend aerobics classes at the YWCA is 130 pounds. We construct a confidence interval (using an alpha of 0.05) of 3.45. The upper and lower limits of our estimate are

a. 130.00 and 133.45

b. 126.55 and 130.45

c. 126.55 and 133.45

d. unknown; these values will depend on the number of women who are truly serious about exercising

17. When using sample means as estimators, we usually estimate the population standard deviation with

a. the sample standard deviation

b. the sampling distribution standard deviation

c. the population parameter

d. the Z score

18. In the formula for finding a confidence interval when the value of the population standard deviation is unknown, we change N to N-1. The reason for this change is

a. to correct for the fact that s is biased

b. the standard deviation of a sample is always greater than the standard deviation of the population

c. the standard deviation of a sample is unbiased

d. sample size is much too large

19. If a researcher changes from the 90% confidence level to the 95% level, the confidence interval will

a. widen

b. decrease in width

c. not be affected

d. widen only if N is greater than 100

20. The central problem in the case of one sample hypothesis test is to determine

a. if a sample is random

b. if sample statistics are the same as those of the sampling distribution

c. if parameters are representative of population

d. if a sample came from a population with a certain characteristic

21. Like estimation procedures, hypothesis testing involves the risk that the sample

a. may not be representative

b. may not be biased

c. may be too large

d. may not be significant

22. The research hypothesis (H1) typically states what the researcher expects to find and

a. contradicts the null hypothesis

b. verifies on the null hypothesis

c. modifies the null hypothesis

d. is unrelated to the null hypothesis

23. If we reject a null hypothesis of "no difference" at the 0.05 level

a. the odds are 20 to 1 in our favor that we have made a correct decision

b. the null hypothesis is true

c. the odds are 5 to 1 in our favor that we have made a correct decision

d. the research hypothesis is true

24. The critical region is

a. the area under the curve that contains "non-rare" events

b. the area under the curve that includes those values of a sample statistic that will lead to rejection of the null.

c. a confidence interval

d. a law that states that the shape of the sampling distribution is normal

25. In tests of significance, if the test statistic falls in the critical region, we may conclude that

a. the population distribution is normal

b. the null hypothesis can be rejected

c. the research hypothesis is true

d. our sample size was too small

26. If the critical region begins at Z (critical) = 2.56 and the test statistic is - 2.50, we

a. fail to reject the null hypothesis

b. reject the null hypothesis

c.  cannot make a decision because the test statistics is so close to the critical region

d. change the alpha level

27. A sample of people attending a professional football game averages 13.7 years of formal education while the surrounding community averages 12.1. The difference is significant at the .05 level. What could we conclude?

a. the null hypothesis should be accepted

b. the research hypothesis should be rejected

c. the sample is significantly more educated than the community as a whole

d. the alpha level is too low

28. A one-tailed test of significance could be used whenever

a. the researcher can predict a direction for the difference

b. the researcher feels like it

c. the null hypothesis is thought to be true

d. the alpha level exceeds 0.10

29. The t distribution, compared to the Z distribution, is

a. more skewed

b. more peaked for small samples but increasingly like the Z distribution as N increases

c. bimodal

d. flatter for small sample sizes but increasingly like the Z distribution as N increases

30. When testing for the significance of the difference between a sample mean and a population mean, degrees of freedom are equal to

a. N - 1

b. N + 1

c. alpha

d. 1 - alpha

31. In order to reject the null hypothesis when using the t distribution and small samples, we will

a. need a smaller test statistic as compared to larger samples

b. need a larger test statistic as compared to larger samples

c. always use one-tailed tests

d. set alpha very low

32. When testing a single sample mean for significance when the population standard deviation is unknown and sample size is 75, the correct sampling distribution is

a. the t distribution

b. the Z distribution

c. it makes no difference

d. t for a one-tailed test, Z for a two-tailed test

33. If the test statistic does not fall in the critical region, we

a. reject the null hypothesis

b. fail to reject the null hypothesis

c. lower the alpha level and conduct a new test

d. commit a Type I error

34. All tests of hypothesis are based on the assumption that

a. the null hypothesis is false and should be rejected

b. the observed difference is important

c. the null hypothesis is true

d. Type I errors are more serious than Type II errors

35. The central problem in the case of two-sample hypothesis test is to determine

a. if the samples are random

b. if sample statistics are the same as those of the sampling distribution

c. if the parameters are representative of the populations

d. if two populations differ significantly on the trait in question

36. When testing for the significance of the difference between two samples, which is the proper assumption for step 1?

a. random sampling

b. ordinal level of measurement

c. degrees of freedom are zero

d. samples are independent as well as random

37. When testing for the significance of the difference between two sample means, the null hypothesis states

     _       _

a. X1 = X2

b. m > 0

c. m = m

d. s = s

38. When testing for the significance of the difference between two samples, the null hypothesis reminds us that our interest is on differences between the

a. samples

b. populations

c. sampling distributions

d. standard deviations

39. Rejection of the null hypothesis in the two-sample case implies that the

a. samples are different on the trait of interest

b. populations from which the samples are drawn are different on the trait of interest

c. samples are not different on the trait of interest

d. populations from which the samples are drawn are not different on the trait of interest

40. Samples of Republicans and Democrats have been tested for their level of support for welfare reform and the null hypothesis has been rejected. What may we conclude?

a. the difference is significant, there are differences between the parties on this issue

b. the difference is significant, the parties are the same on this issue

c. the difference is not significant

d. a Type I error has occurred

41. When conducting hypothesis tests for two sample means, the test statistic is

a. alpha

b. the difference in sample means

c. the degrees of freedom

d. the difference in the population means

42. When testing for the significance of the difference between two sample means, the standard deviation of the sampling distribution is estimated using

a. population standard deviations

b. the standard error of the means

c. degrees of freedom

d. sample standard deviations corrected for bias

43. Random samples of men and women have been given a scale that measures their support for gun control. Men average 10.2 with standard deviation of 5.3. Women also average 10.2 but their standard deviation is 1.8. How could these results be dealt with appropriately?

a. test the difference in the sample means for statistical significance

b. since the sample means are the same value, there is no need to conduct any tests; these results cannot be significant

c. a one-tailed test of significance is called for

d. a test of significance with a very high alpha level (a > 0.10) is called for

44. A researcher conducted a survey to determine if older people have different feelings about abortion than younger people. He used an alpha level of 0.05 (Z critical = 1.96) to test for significance and found that his computed test statistic was 2.76. He may conclude that

a. the difference occurred by random chance

b. the difference did not occur by random chance

c. the samples are not independent

d. the alpha level was too low

45. When testing for the significance of the difference between sample means with small samples, the proper sampling distribution is

a. the alpha distribution

b. the beta distribution

c. the Z distribution

d. the t distribution

46. From a University population, random samples of 45 seniors and 37 freshman have been given a scale that measures sexual experiences. The freshman report an average of 1.6 sexual partners over their lifetimes while seniors report an average of 2.5 partners. The t (obtained) for this difference was -3.56 while the t (critical) was 2.34. What can be concluded?

a. there is no significant difference between the classes

b. seniors and freshman are significantly different in their sexual experiences

c. freshman are more sexually active

d. sexual mores are deteriorating

47. Random samples of 1546 men and 1678 women have been given a scale that measures support of legal abortion. Men average 12.45 and women average 12.46 and the difference is significant at the 0.05 level. What can we conclude?

a. There is an important difference between men and women on this issue.

b. Because of the large sample sizes, these results may be statistically significant but trivial.

c. The difference should be re-tested with a one-tailed test

d. The difference should be re-tested at a higher alpha level

48. The text reports the results of a test for the significance of the difference in average income for random samples of males and females. Males earned an average of about $12,000 more per year and the Z score computed in step 4 was 8.09. Given these results, which of the following is a reasonable conclusion?

a. The difference is statistically significant, large, and important

b. The difference is not statistically significant and was probably caused by random chance

c. There is no gender gap in income in the United States

d. This difference is statistically significant but quite small.

For questions 1 and 2 below, construct the 95% confidence interval estimate to the population. Assume that the results are based on a nationally representative sample. Express the estimate in a sentence.

1. Of the 1220 respondents for whom we have information, 178 said that they had been divorced at least once.

2. Four hundred and thirty two of the 668 respondents questioned said that they favored capital punishment for people convicted of murder. Ten years ago, in response to the same question, 378 out of 703 people were in favor of capital punishment. Has support for capital punishment risen over the ten year period?

3. Do students who are members of fraternities or sororities have GPAs different from the student body as a whole? A random sample of 123 "Greeks" has been selected from the student body of a large university. The GPA for the student body as a whole is 2.59 and the mean for the sample is 2.47 with a standard deviation of 0.34. Is the difference statistically significant? Follow the five-step model and state all important decisions. Make sure that you interpret the results in terms of the original research question.

4. A researcher selected a sample of 56 former student leaders from a list of graduates of a large university. She discovered that it had taken an average of 4.97 years for these graduates to finish their degrees, with a standard deviation of 1.23. The average for the entire student body is 4.56 years. Is the difference statistically significant? Follow the five-step model and state all important decisions. Make sure that you interpret the results in terms of the original research question.

5. A sample of students attending a large university has been selected. Is there a statistically significant difference between Liberal Arts majors and other students on average number of books (other than those required by course work) read per year? Use the five step model and write a sentence or two interpreting your results.

Liberal Arts      Other

_                   _

X= 16.2            X = 13.7

s1 = 2.3            s2 = 9.0

N1 = 236         N2 = 321

6. A scale measuring confidence in the media was administered to a sample. Is there a statistically significant difference between Democrats and Republicans on the scale? Higher scores on the scale indicate greater confidence. Use the five step model and write a sentence or two interpreting your results.

Democrats      Republicans

_                       _

X= 8.5             X= 7.8

s1 = 1.5          s2 = 1.1

N1 = 36          N2 = 35

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