A sample survey by the Pew Internet and American Life Project asked a random sample of adults about use of the Internet.

One question was whether the subject had a broadband Internet connection at home.

Here is a two-way table of home broadband use by type of community:

1. Give a 95% large sample confidence interval for the difference between the proportion of all rural and urban adults who have a home broadband connection.

A. 0.1640 to 0.2574

B. 0.1535 to 0.2679

C. 0.3597 to 0.4741

D. 0.1547 to 0.2666

2. What proportion of each of the three groups in the sample have home broadband?

Match your answers below:

1. 0.5236

2. 0.1749

3. 0.2290

4. 0.4901

5. 0.0791

6. 0.3102

7. 0.5208

8. 0.3015

9. 0.2368

10. 0.1255

A. Urban

B. Suburban

C. Rural

3. Are these statistically significant differences among these proportions?

The hypotheses for the test are:

A. H0 : pr = ps = pu vs. Ha : not all proportions are equal.

B. H0 : pr = ps = pu vs. Ha : no two proportions are equal.

C. H0 : There is no relationship between home broadband used and type of community;

Ha : There is some relationship between home broadband used and type of community.

D. H0 : pr = ps = pu = 1/3 vs. Ha : not all proportions are 1/3.

4. Give the test statistic and its P-value.

A. χ2 = 7.925, P < 0.0005

B. χ2 = 7.925, 0.0005 < P < 0.001

C. χ2 = 62.813, P < 0.0005

D. χ2 = 62.813, 0.0005 < P < 0.001

5. True or False:

The following conclusion can be made:

"The relationship between home broadband used and type of community is statistically significant."

Sample surveys on sensitive issues can give different results depending on how the question is asked. A University of Wisconsin study divided 2400 respondents into 3 groups at random. All were asked if they had ever used cocaine. One group of 800 was interviewed by phone; 21% said they had used cocaine. Another 800 people were asked the question in a one-on-one personal interview; 25% said "Yes."

The remaining 800 were allowed to make an anonymous written response; 28% said "Yes." Are there statistically significant differences among these proportions?

6. Which of the following are the correct hypotheses?

A. H0 : There is no relationship between the way of interviewing and the answer.

Ha : Anonymity raises the proportion of "yes".

B. H0 : There is no relationship between the way of interviewing and the answer.

Ha : There is relationship between the way of interviewing and the answer.

C. H0 : There is no relationship between the way of interviewing and the answer.

Ha : In phone interview, the proportion of "yes" is the lowest.

D. H0 : There is relationship between the way of interviewing and the answer.

Ha : The proportions of "yes" are not the same in the three ways of interviewing.

7. The two-way table of counts is,

(Cell format: upper value = observed count, mid value = expected count, lower value = contribution to Χ2)

A.

Phone One-to-one Anonymous Total

Yes 168

21

4 200

25

1.201 224

218

3.512 592

Other answers 632

79

2.211 600

75

0.11 576

72

0.091 1808

Total 800 800 800 2400

B.

Phone One-to-one Anonymous Total

Yes 168

7

3.991 200

8.33

0.025 224

9.33

3.501 592

Other answers 632

26.33

1.427 600

25

0.012 576

24

1.180 1808

Total 800 800 800 2400

C.

Phone One-to-one Anonymous Total

Yes 168

197.33

4.367 200

197.33

0.036 224

197.33

3.605 592

Other answers 632

602.67

1.427 600

602.67

0.012 576

602.67

1.180 1808

Total 800 800 800 2400

D.

Phone One-to-one Anonymous Total

Yes 168

28.38

3.911 200

33.78

0.025 224

37.84

3.511 592

Other answers 632

34.96

1.521 600

33.19

0.009 576

31.86

1.002 1808

Total 800 800 800 2400

8. The test statistic and P-value are:

A. Χ2 = 10.627, 2 degrees of freedom, 0.0025 < p < 0.005.

B. Χ2 = 10.627, 6 degrees of freedom, 0.05 < p < 0.1.

C. Χ2 = 3.26, 2 degrees of freedom, 0.15 < p < 0.2.

D. Χ2 = 3.26, 1 degrees of freedom, 0.05 < p < 0.1.

9. The following conclusion can be made:

A. There is no relationship between the way of asking and the answer.

B. There is a difference in proportions of "yes" answers in the three ways of asking.

The main difference is in lower proportion of "yes" answers in phone interviews.

C. There are equal proportions of "yes" answers in all 3 ways of asking.

D. The main difference between the 3 ways of asking is that in one-to-one interview there is greater proportion of "yes" answer.

"Do you favor or oppose the death penalty for persons convicted of murder?" When the General Social Survey asked this question, the responses of people whose highest education was a bachelor's degree and of people with a graduate degree were as follows:

Favor Oppose

Bachelor 135 71

Graduate 64 50

Is there evidence that the proportions of all people at these levels of education who favor the death penalty differ?

10. Find the sample proportion of bachelors who favor the death penalty. Give your answers to 3 decimal places.

11. Find the sample proportion of graduates who favor the death penalty. Give your answers to 3 decimal places.

12. The z statistic and its P-value for the test are:

A. z = 1.277, p = 0.1003

B. z = 1.277, p = 0.2006

C. z = 1.661, p = 0.0485

D. z = 1.659, p = 0.097

13. "There is evidence that the proportions of all people at these levels of education who favor the death penalty differ".

True or False?

14. Is there evidence that the opinions of all people at these levels of education differ?

The expected values in the two-way table are:

A.

Favor Oppose

Bachelor 65.53 34.47

Graduate 56.14 43.86

B.

Favor Oppose

Bachelor 67.84 58.68

Graduate 32.16 41.3

C.

Favor Oppose

Bachelor 128.11 77.89

Graduate 70.89 43.11

D.

Favor Oppose

Bachelor 42.19 22.19

Graduate 20 15.63

15. The test statistic and P-value are:

A. Χ2 = 2.7539, one degree of freedom 0.05 < p < 0.1

B. Χ2 = 2.7509, four degrees of freedom p > 0.25

C. Χ2 = 2.7509, two degrees of freedom p > 0.25

D. Χ2 = 7.5675, one degree of freedom 0.005 < p < 0.01

16. Here is more information about Internet use by students at Penn State, based on a random sample of 1852 undergraduates.

Explain why it is not correct to use a chi-square test on this table to compare the University Park and commonwealth campuses. (Select TWO answers)

It is not correct to use a chi-square test on this table to compute the University Park and commonwealth campuses, because:

A. More than 20% of the expected counts are less than 5.

B. Some of the expected counts are less than 1.

C. Each respondent may participate in more than one category of Internal use.

D. The cell counts do not add to 1852.

Are you a morning person, an evening person, or neither? Does this personality trait affect how well you perform? A sample of 100 students took a psychological test that found 16 morning people, 30 evening people, and 54 who were neither. All the students then took a test of their ability to memorize at 8 a.m. and again at 9 p.m. Analyze the score at 8 a.m. minus the score at 9 p.m.

17. Identify the populations and the response variable.

A. The populations are the 100 students who took the test and the variable is whether they are morning or evening people.

B. The populations are the three groups of students and the variable is the time of day they memorize better.

C. The populations are the students in the three groups (evening persons, morning persons and neither) and the variable is their score for memorize ability at 8 A.M. minus their score at 9 P.M.

18. What is the value of I?

19. What are the values of ni?

A. n1 = 100, n2 = 100 and n3 = 100.

B. n1 = 8, n2 = 9 and n3 = 1.

C. n1 = 16, n2 = 30 and n3 = 54.

20. What is the value of N?

21. What is the value of the ANOVA F numerator degrees of freedom?

22. What is the value of the denominator degrees of freedom?

More rain for California? Exercise 24.30 describes a randomized experiment carried out by Kenwyn Suttle and his coworkers to examine the effects of additional water on California grassland.

The experimental units are 18 plots of grassland, assigned at random among three treatments: added water in the winter wet season, added water in the spring dry season, and no added water (control group).

Field experiments, unlike laboratory experiments, are exposed to variations in the natural environment.

The experiment therefore continued over 5 years, 2001 to 2005.

Table 24.6 gives data on the total plant biomass (grams per square meter) that grew on each plot during each year.

The “Plot”column shows how the random assignment of 18 of the 36 available plots worked.

Exercises 24.38 to 24.40 are based on this information.

23. Examine the data for the year 2004.

The conditions for ANOVA inference are not met.

In what way do these data fail to meet the conditions?

A. The spring biomass distribution has an outlier.

B. The samples are too small.

C. The populations do not have equal standard deviations.

D. The spring biomass distributions has an outlier and the standard deviation violates our rule of thumb.

Many states require schoolchildren to take regular statewide tests to assess their progress.

Children with learning disabilities who read poorly may not do well on mathematics tests because they can’t read the problems.

Most states allow “accommodations” for learning-disabled children.

Randomly assign 100 learning-disabled children in equal numbers to three types of accommodation and a control group: math problems are read by a teacher; by a computer; by a computer that also shows a video; and standard test conditions.

Compare the mean scores on the state mathematics assessment.

24. Identify the populations and the response variable.

A. The populations are learning disabled children with each of the four accommodations.

The variable is the score on the state math exam.

B. The populations are 4 different groups of learning disabled children, and the variable is the accommodation that was used.

C. The populations are the types of accommodation and the variable is the score on the state math exam.

D. The population are learning disabled children and the variable is the type of accommodation that was used.

25. What is the value of I?

Give your answer as a whole number.

Fill in the blank:

26. What are the values of ni?

A. n1 = n2 = n3 = n4 = 100

B. n1 = n2 = n3 = n4 = 4

C. n1 = n2 = n3 = n4 = 25

D. n1 = n2 = 4, n3 = 25, n4 = 100

27. What is the value of N?

Give your answer as a whole number.

Fill in the blank:

28. What is the value of the ANOVA F numerator degrees of freedom?

Give your answer as a whole number.

Fill in the blank:

29. What is the value of the ANOVA F denominator degrees of freedom?

Give your answer as whole number.

Fill in the blank: