Inference Review 3 - Chapter 11
Multiple Choice
Scenario 11-7
Number of re-arrestsNone / One / Two / Three or more
Assigned Treatment / Arrest / 175 / 36 / 2 / 1
Citation / 181 / 33 / 7 / 3
Advise/Separate / 187 / 24 / 1 / 0
When a police officer responds to a call for help in a case of spousal abuse, what should the officer do? A randomized controlled experiment in Charlotte, North Carolina, studied three police responses to spousal abuse: advise and possibly separate the couple, issue a citation to the offender, and arrest the offender. The effectiveness of the three responses was determined by re-arrest rates. The table below shows these rates.
1. Use Scenario 11-7. Even though Puerto Rico is a territory of the United States, there are many cultural differences
between the states on the continent of North America and the Caribbean island of Puerto Rico. These differences include the way consumers respond to problems with purchases. Two researchers surveyed owners of VCRs in the Northeastern United States and in Puerto Rico. They asked those who had experienced problems with their VCRs and whether they had complained. The results are given in the table below.
Complained?Yes / No
Region / N.E. United States / 330 / 94
Puerto Rico / 64 / 33
The cell that contributes most to the c2 statistic is
A.Americans in the Northeastern United States who complained. B.Puerto Ricans who complained. C.Americans in the Northeastern United States who did not complain. D.Since the data form a 2 ´ 2 table, all cells contribute equally to the statistic. E.Puerto Ricans who did not complain.
2. Use Scenario 11-7. Suppose we wish to test the null hypothesis that the proportion of subsequent arrests is the same regardless of the treatment assigned. Which of the following statements is true?
A.We cannot test this hypothesis because this is an experiment, not a random sample. B.The test of the null hypothesis will have a very small P-value (below 0.0001) because there were so few cases where there was more than one re-arrest. C.We should eliminate the last column, since there are so few entries in that column. D.The test of the null hypothesis will have a very small P-value (below 0.0001) because the counts in each row are not identical. E.We cannot test this hypothesis because the expected cell counts are less than 5 in some of the cells.
Scenario 11-8 All current-carrying wires produce electromagnetic (EM) radiation, including the electrical wiring running into, through, and out of our homes. High-frequency EM radiation is thought to be a cause of cancer; the lower frequencies associated with household current are generally assumed to be harmless. To investigate this, researchers visited the addresses of children in the Denver area who had died of some form of cancer (leukemia, lymphoma, or some other type. and classified the wiring configuration outside the building as either a high-current configuration (HCC. or as a low-current configuration (LCC.. Here are some of the results of the study.
Cancer typeLeukemia / Lymphoma / Other cancers
HCC / 52 / 10 / 17
LCC / 84 / 21 / 31
Computer software was used to analyze the data. The output is given below. It includes the cell counts, the expected cell counts, and the value of the c2 statistic. In the table, expected counts are printed below observed counts.
Leukemia / Lymphoma / Other Cancers / TotalHCC / 52 / 10 / 17 / 79
49.97 / 11.39 / 17.64
LCC / 84 / 21 / 31 / 136
86.03 / 19.61 / 30.36
TOTAL / 136 / 31 / 48 / 215
Chi-Sq = 0.435
3. Use Scenario 11-8. Which of the following intervals contains the P-value of the test?
A.between 0.05 and 0.10. B.between 0.01 and 0.05. C.between 0.10 and 0.20. D.less than 0.01. E.larger than 0.20.
4. Use Scenario 11-8. The appropriate degrees of freedom for the c2 statistic is
A.2. B.5. C.1. D.4. E.3.
5. Use Scenario 11-8. Which of the following may we conclude, based on the test results?
A.There is weak evidence that HCC causes cancer in children. B.There is not much evidence of an association between wiring configuration and the type of cancer that caused the deaths of children in the study. C.Leukemia is the most common type of cancer among children. D.HCC either causes cancer directly or is a major contributing factor to the development of cancer in children. E.There is strong evidence of an association between wiring configuration and the chance a child will develop some form of cancer.
Scenario 11-2 To test the effectiveness of a certain computer software’s random number generator, I randomly select 1000 numbers from a standard Normal distribution. I classify these 1000 numbers according to whether their values are at most –2, between –2 and 0, between 0 and 2, or at least2. The results are given in the following table. The expected counts, based on the 68-95-99.7 rule, are given as well.
Observed Count / 18 / 492 / 468 / 22Expected Count / 25 / 475 / 475 / 25
To test to see if the distribution of observed counts differs significantly from the distribution of expected counts, we use a c2 test.
6. Use Scenario 11-2. The value of the c2 statistic is found to be 3.03. The P-value of the test is
A.between 0.10 and 0.20. B.between 0.01 and 0.05. C.less than 0.01. D.greater than 0.20. E.between 0.05 and 0.10.
7. Use Scenario 11-2. For this test, the c2 statistic has approximately a chi-square (c2) distribution. How many degrees of freedom does this distribution have?
A.1000. B.4. C.999. D.7. E.3.
Scenario 11-9 Recent revenue shortfalls in a Midwestern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 25% tuition increase. It was determined that such an increase was needed simply to compensate for the lost support from the state. Random samples of 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors from the university were asked whether or not they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university’s budget at current levels. The results are given in the following table.
YearFreshman / Sophomore / Junior / Senior
Strongly / Yes / 39 / 36 / 29 / 18
Opposed? / No / 11 / 14 / 21 / 32
8. Use Scenario 11-9. Which of the following are conditions that must be met before performing a chi-square test on these data?
I. The sample is large enough so that all observed counts are greater than 5.
II. The data come from independent random samples of Freshmen, Sophomores, Juniors, and Seniors.
III. The populations from which the samples were taken are Normally distributed.
A.I only B.II only C.All three conditions must be met. D.III only E.I and III only
Cookie Brand / A / B / C / DNumber of choosing brand / 26 / 18 / 24 / 28
Scenario 11-4
Ida wants to know if people show a preference for one brand of ready-made chocolate chip cookie dough over another. To test this, she bakes eight dozen cookies from dough made by each of four manufacturers which she labels brands A, B, C, and D, to conceal the name of the company from the tasters. She then selects a simple random sample of 96 students at her school to try each brand of cookie and choose the brand they like best. The cookies are tasted in random order. Here are her results:
9. Use Scenario 11-4. The brand category that contributes the largest component to the c2 statistic is
A.B. B.A. C.C. D.D. E.All four components are roughly equal.
Cookie BrandA / B / C / D / Total
Males / 4 / 6 / 13 / 15 / 38
Females / 22 / 12 / 11 / 13 / 58
Total / 26 / 18 / 24 / 28 / 96
Scenario 11-5
Ida wants to know if males and females prefer different brands of ready-made chocolate-chip cookie dough. She bakes eight dozen cookies from dough made by each of four manufacturers which she labels brands A, B, C, and D. She then selects a simple random sample of 96 students, records their gender, gives them one cookie of each brand and asks which brand they like best. Here are her results:
10. Use Scenario 11-5. The conditional distribution for preferred cookie brand among males (in percents) is given by which of the following?
A.A: 4%; B: 6%; C: 13%; D: 15% B.A: 27%; B: 19%; C: 25%; D: 29% C.A: 11%; B: 16%; C: 34%; D: 39% D.A: 23%; B: 13%; C: 11%; D: 14% E.A: 38%; B: 21%; C: 19%; D: 22%
11. Use Scenario 11-5. If we want to compare the conditional distributions for preferred cookie brand among males to the same distribution for females, which of the following is an appropriate graph to use?
A.Segmented bar graphs B.Scatterplot C.Parallel dotplots D.Side-by-side histograms E.Back-to-back stemplots
Scenario 11-10 A random sample of 200 Canadian students were asked about their hand dominance and whether they suffer from allergies. Here are the results:
Allergies?Yes / No
Hand dominance / Ambidextrous / 12 / 7
Left-handed / 11 / 9
Right-handed / 95 / 66
12. Use Scenario 11-10. Which of the following are appropriate null and alternative hypotheses for these data?
A. / Ho: The distribution of hand dominance is the same for people with allergies and people without allergies.H–a: Hand dominance and allergies are independent.
B. / Ho: There is no association between hand dominance and allergies.
H–a: There is an association between hand dominance and allergies.
C. / Ho: There is an association between hand dominance and allergies.
H–a: There is no association between hand dominance and allergies.
D. / Ho: The distribution of hand dominance is different for people with allergies and people without allergies.
H–a: The distribution of hand dominance is the same for people with allergies and people without allergies.
E. / Ho: Hand dominance and allergies are not independent.
H–a: Hand dominance and allergies are independent.
Scenario 11-1 Do certain car colors attract the attention of police more than others, so that they are more likely to get speeding tickets? A few years ago a curious newspaper columnist tabulated the car color on a random sample of 120 speeding citations at the local courthouse. Here are his results.
Color / Red / White/Silver / Gray/Black / OtherNumber of speeding tickets / 16 / 33 / 39 / 32
He then went to the state motor vehicle registry and obtained data on the distribution of car colors for all cars registered in his state:
Color / Red / White/Silver / Gray/Black / OtherPercentage of cars on highway / 14% / 35% / 23% / 28%
13. Use Scenario 11-1. To answer the question posed above about car color and speeding tickets, the appropriate null hypothesis is:
A.The observed counts are all equal to 30. B.The observed counts are equal to the expected counts. C.The observed number of speeding tickets is the same for all four color groups. D.The distribution of car colors for the speeding citations is the same as the distribution of colors for cars on the highway. E.At least one of the four car color percentages is different from the other three.
14. Use Scenario 11-1. Which of the following are the correct expected counts for speeding tickets under the null hypothesis?
A. B. C. D. E.
15. Which of the following is a condition that must be satisfied to use a chi-square goodness-of-fit test?
A.The number of categories is small relative to the number of observations. B.The expected count for each category is greater than 5. C.The population distribution is approximately Normal. D.The sample size is greater than 30. E.The expected count is the same for each category.
Scenario 11-11 Random samples of male and female high school students were asked to identify their favorite food group. Here are the results:
GenderFemale / Male
Favorite Food Group / Carbohydrates / 45 / 21
Dairy / 20 / 17
Fruits and vegetables / 14 / 9
Proteins / 7 / 17
Expected counts for each cell are given in the following table:
GenderFemale / Male
Favorite Food Group / Carbohydrates / 37.8 / 28.2
Dairy / 21.2 / 15.8
Fruits and vegetables / 13.2 / 9.8
Proteins / 13.8 / 10.2
16. Use Scenario 11-11. Which of the following are appropriate null and alternative hypotheses for these data?
A. / Ho: Favorite food group and gender are not independent.Ha: Favorite food group and gender are independent.
B. / Ho: The distribution of favorite food group is not the same for the two genders.
Ha: The distribution of favorite food group is the same for the two genders.
C. / Ho: The distribution of favorite food group is the same for both genders.
Ha: The distribution of favorite food group is not the same for both genders.
D. / Ho: favorite food group and gender are independent.
Ha: There is no association between favorite food group and gender.
E. / Ho: The distribution of gender is the same for all four food groups.
Ha: The distribution of gender is different for at least one food group.
17. Use Scenario 11-11. Which of the following cells contributions the most to the chi-square statistic?