Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) 1) A) B) C) D) Decide whether or not the conditions and assumptions for inference with a chi-square test are satisfied. If they are not, then state why. 2) A researcher performed a study to determine whether an association exists between sex and blood 2) type. He obtained the following data from a random sample. A) No, because it is not possible to find the residuals. B) No, because the expected cell frequency condition is violated. C) No, because the data are quantitative. D) Yes E) No, because the sample does not appear to be random. Perform the appropriate chi-square test and state your conclusion. 3) Responses to a survey question are broken down according to employment status and the sample results are given below. Are the response and employment status independent? Yes No Undecided Employed 40 15 5 Unemployed 10 25 10 3) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine the null and alternative hypotheses for the study that produced the data in the table. 4) The Book Industry Study Group, Inc. performs sample surveys to obtain information on characteristics of book readers. A book reader is defined to be one who read one or more books in the six months prior to the survey; a non-book reader is defined to be one who read newspapers or magazines but no books in the six months prior to the survey; a nonreader is defined to be one who did not read a book, newspaper, or magazine in the six months prior to the survey. The following data were obtained from a random sample of 1429 persons 16 years old and over in an effort to determine whether or not the proportions of book readers, non-book readers, and non-readers are the same for each income bracket. 4) 1
A) H0 : There is a relationship between household income and book readership. HA : Household income and book readership are not related. B) H0 : There is no relationship between household income and book readership. HA : Household income and book readership are not related. C) H0 : The classifications do not have the same distribution for each household income bracket. HA : The classifications have the same distribution for each household income bracket. D) H0 : Household income and book readership are independent. HA : Household income and book readership are not dependent. E) H0 : The classifications have the same distribution for each household income bracket. HA : The classifications do not have the same distribution for each household income bracket. Perform the indicated goodness-of-fit test. 5) Test the claim that the responses occur with percentages of 15%, 20%, 25%, 25%, and 15% respectively. 5) Response A B C D E Frequency 12 15 16 18 19 6) Test the claim that the responses occur with percentages of 15%, 20%, 25%, 25%, and 15% respectively. 6) Response A B C D E Frequency 12 15 16 18 19 2
Provide an appropriate response. 7) A random sample of 800 adults was asked the following question: "Do you think current laws concerning the use of cloning for medical research are too strict, too lenient, or about right?" The pollsters also classified the respondents with respect to highest education level attained: high school, 2-year college degree, 4-year degree, or advanced degree. We wish to know if attitudes on cloning are related to education level. (All the conditions are satisfied - don't worry about checking them.) Suppose the expected counts had not been given. Show how to calculate the expected count in the first cell (106.01). 7) 8) A random sample of 800 adults was asked the following question: "Do you think current laws concerning the use of cloning for medical research are too strict, too lenient, or about right?" The pollsters also classified the respondents with respect to highest education level attained: high school, 2-year college degree, 4-year degree, or advanced degree. We wish to know if attitudes on cloning are related to education level. (All the conditions are satisfied - don't worry about checking them.) Write appropriate hypotheses. 8) 3
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine the null and alternative hypotheses for the study that produced the data in the table. 9) A car insurance company performed a study to determine whether an association exists between age and the frequency of car accidents. They obtained the following sample data. 9) A) H0 : Number of accidents in the past three years and age group are independent. HA : Number of accidents in the past three years and age group are not independent. B) H0 : Number of accidents in the past three years and age group are dependent. HA : Number of accidents in the past three years and age group are not dependent. C) H0 : Number of accidents in the past three years has the same distribution for each age group. HA : Number of accidents in the past three years does not have the same distribution for each age group. D) H0 : Number of accidents in the past three years and age group are not dependent. HA : Number of accidents in the past three years and age group are independent. E) H0 : Number of accidents in the past three years and age group are independent. HA : Number of accidents in the past three years and age group are not dependent. 10) A candy company claims that its bags of mixed suckers are 20% strawberry, 30% cherry, 15% apple, 10% lemon, and 25% grape. A bag was purchased, and the number of each type of flavor was recorded in the chart below. 10) Flavor Count Strawberry 31 Cherry 15 Apple 17 Lemon 15 Grape 22 A) H0: The distribution of flavors is the same as the distribution claimed by the company. HA: The distribution of flavors is not the same as the distribution claimed by the company. B) H0: The flavors and counts are independent. HA: The flavors and counts are not independent. C) H0: The distribution of flavors is not uniform. HA: The distribution of flavors is uniform. D) H0: The distribution of flavors is uniform. HA: The distribution of flavors is not uniform. E) H0: The distribution of flavors is not the same as the distribution claimed by the company. HA: The distribution of flavors is the same as the distribution claimed by the company. 4
A chi-square test has been performed on the given data, with the results shown. Calculate the standardized residuals for the data and comment on your findings. 11) The sample data below was tested to determine whether car color is related to the 11) likelihood of being in an accident. Red Blue White Car has been in accident 49 11 30 Car has not been in accident 51 89 70 Test statistic: 2 =34.38 P-value = 3.42 10-8 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Decide which chi-square test (goodness-of fit, homogeneity, or independence) would be most appropriate for the given situation. 12) Tests for adverse reactions to a new drug yielded the results given in the table. The data will be 12) analyzed to determine if there is sufficient evidence to conclude that an association exists between the treatment (drug or placebo) and the reaction (whether or not headaches were experienced). Drug Placebo Headaches 11 7 No headaches 73 91 A) Independence B) Goodness-of-fit C) Homogeneity Provide an appropriate response. 13) A random sample of 337 college students was asked whether or not they were registered to vote. We wonder if there is an association between a student's sex and whether the student is registered to vote. The data are provided in the tables below (expected counts are in parentheses). (All the conditions are satisfied - don't worry about checking them.) 13) Men Women Total Registered 104 (102) 147 (149) 251 Not Registered 33 (35) 53 (51) 86 Total 137 200 337 The calculated statistic is 2 = 0.249. Supposed the expected values had not been given. Show how to calculate the expected number of men who are registered to vote. 5
Perform the appropriate chi-square test and state your conclusion. 14) A researcher performed a study to determine whether an association exists between gender and blood type. He obtained the following sample data. 14) Does the data provide sufficient evidence to conclude that an association exists between gender and blood type? 15) Use the sample data below to test whether car color affects the likelihood of being in an accident. Red Blue White Car has been in accident 28 33 36 Car has not been in accident 23 22 30 15) Provide an appropriate response. 16) In a study of how the burden of poverty varies among U. S. regions, a random sample of 1000 individuals from each region of the United States recently yielded the information on poverty (based on defining the poverty level as an income below $10,400 for a family of 4 people). The data are provided in the table to the right. (All the conditions are satisfied - don't worry about checking them.) Suppose the expected values had not been given. Show exactly how to calculate the expected count in the first cell. 16) 6
A chi-square test has been performed on the given data, with the results shown. Calculate the standardized residuals for the data and comment on your findings. 17) The sample data below was tested to determine whether car color is related to the 17) likelihood of being in an accident. Red Blue White Car has been in accident 49 11 30 Car has not been in accident 51 89 70 Test statistic: 2 =34.38 P-value = 3.42 10-8 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Decide which chi-square test (goodness-of fit, homogeneity, or independence) would be most appropriate for the given situation. 18) A candy company claims that its bags of mixed suckers are 20% strawberry, 30% cherry, 15% 18) apple, 10% lemon, and 25% grape. A bag was purchased, and the number of each type of flavor was recorded in the chart below. Flavor Count Strawberry 31 Cherry 15 Apple 17 Lemon 15 Grape 22 A) Goodness-of-fit B) Homogeneity C) Independence 19) A die, suspected of being unfair, was rolled 50 times. The number of times each face appeared was recorded in the following table. 19) Face Count 1 8 2 10 3 9 4 11 5 5 6 7 A) Independence B) Goodness-of-fit C) Homogeneity Provide an appropriate response. 20) According to Masterfoods, Inc., peanut M&M's are 12% brown, 15% yellow, 12% red, 23% blue, 23% orange, and 15% green. On a Saturday when you have run out of statistics homework, you decide to test this claim. You purchase a medium bag of peanut M&M's and find 39 browns, 44 yellows, 36 red, 78 blue, 73 orange, and 48 greens. Test an appropriate hypothesis and state your conclusion. 20) 7
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Decide which chi-square test (goodness-of fit, homogeneity, or independence) would be most appropriate for the given situation. 21) A researcher performed a study to determine whether an association exists between sex and blood 21) type. He obtained the following sample data. 160 140 140 130 A) Homogeneity B) Independence C) Goodness-of-fit Interpret the results of the chi-square test. 22) Tests for adverse reactions to a new drug yielded the results given in the table. 22) Drug Placebo Headaches 11 7 No headaches 73 91 2 = 1.798; P-value = 0.1799 The data will be analyzed to determine if there is sufficient evidence to conclude that an association exists between the treatment (drug or placebo) and the reaction (whether or not headaches were experienced). A) Do not reject the null hypothesis. Report that there is insufficient evidence to conclude that the distribution of headaches is uniform for the drug and placebo. B) Do not reject the null hypothesis. Report that there is insufficient evidence to conclude that treatment and reaction are dependent. C) Reject the null hypothesis. Report that there is insufficient evidence to conclude that treatment and reaction are dependent. D) Reject the null hypothesis. Report that there is sufficient evidence to conclude that treatment and reaction are dependent. E) Do not reject the null hypothesis. Report that there is sufficient evidence to conclude that treatment and reaction are dependent. Provide an appropriate response. 23) According to information from a college admissions office, 62% of the students there attended public high schools, 26% attended private high schools, 2% were home schooled, and the remaining students attended schools in other countries. Among this college's Honors Graduates last year there were 47 who came from public schools, 29 from private schools, 4 who had been home schooled, and 4 students from abroad. Is there any evidence that one type of high school might better equip students to attain high academic honors at this college? Test an appropriate hypothesis and state your conclusion. 23) 8
24) A random sample of 337 college students was asked whether or not they were registered to vote. We wonder if there is an association between a student's sex and whether the student is registered to vote. The data are provided in the tables below (expected counts are in parentheses). (All the conditions are satisfied - don't worry about checking them.) 24) Men Women Total Registered 104 (102) 147 (149) 251 Not Registered 33 (35) 53 (51) 86 Total 137 200 337 The calculated statistic is 2 = 0.249. Supposed the expected values had not been given. Show how to calculate the expected number of men who are registered to vote. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine the null and alternative hypotheses for the study that produced the data in the table. 25) Tests for adverse reactions to a new drug yielded the results given in the table. The data will be analyzed to determine if they provide sufficient evidence to conclude that an association exists between the treatment (drug or placebo) and the reaction (whether or not headaches were experienced). 25) Drug Placebo Headaches 11 7 No headaches 73 91 A) H0 : The occurrence of headaches is dependent upon the drug. HA : The occurrence of headaches is not dependent upon the drug. B) H0 : The distribution of headaches is different for the drug and the placebo. HA : The distribution of headaches is the same for the drug and the placebo. C) H0 : The drug is related to the occurrence of headaches. HA : The drug is not related to the occurrence of headaches. D) H0 : There is a relationship between the drug and occurrence of headaches. HA : There is no relationship between the drug and occurrence of headaches. E) H0 : The drug is independent from the occurrence of headaches. HA : The drug is not independent from the occurrence of headaches. 9
26) Tests for adverse reactions to a new drug yielded the results given in the table. The data will be analyzed to determine if they provide sufficient evidence to conclude that an association exists between the treatment (drug or placebo) and the reaction (whether or not headaches were experienced). 26) Drug Placebo Headaches 11 7 No headaches 73 91 A) H0 : There is a relationship between the drug and occurrence of headaches. HA : There is no relationship between the drug and occurrence of headaches. B) H0 : The occurrence of headaches is dependent upon the drug. HA : The occurrence of headaches is not dependent upon the drug. C) H0 : The drug is independent from the occurrence of headaches. HA : The drug is not independent from the occurrence of headaches. D) H0 : The drug is related to the occurrence of headaches. HA : The drug is not related to the occurrence of headaches. E) H0 : The distribution of headaches is different for the drug and the placebo. HA : The distribution of headaches is the same for the drug and the placebo. Provide an appropriate response. 27) Is the height of a man related to his weight? The regression analysis from a sample of 26 men is shown. (Show work. Don't write hypotheses. Assume the assumptions for inference were satisfied.) What is the P-value? 27) 10
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the required confidence interval for the slope of the regression equation. You may assume the conditions for regression inference are satisfied. 28) A grass seed company conducts a study to determine the relationship between the density of seeds 28) planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight similar plots of land are selected and each is planted with a particular density of seed. One month later the quality of each lawn is rated on a scale of 0 to 100. The regression analysis is given below. Find a 95% confidence interval for the slope of the regression line. Dependent variable is: Lawn Quality R-squared = 36.0% s = 9.073602 with 8-2 = 6 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Constant 33.14815 7.510757 4.413423 0.004503 Seed Density 4.537037 2.469522 1.837213 0.115825 A) (-1.30, 10.38) B) (27.10, 39.18) C) (14.77, 51.53) D) (-0.26, 9.34) E) (-1.51, 10.58) 29) It's common for a movie's ticket sales to open high for the first couple of weeks, then gradually taper off as time passes. Hoping to be able to better understand how quickly sales decline, an industry analyst keeps track of box office revenues for a new film over its first 20 weeks. What inference method might provide useful insight? A) t-interval for a mean B) t-interval for slope C) 2 goodness-of-fit test D) 1-proportion z-test E) t-test for linear regression 29) 11
Interpret the given confidence interval. 30) A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight similar plots of land are selected and each is planted with a particular density of seed. One month later the quality of each lawn is rated on a scale of 0 to 100. The regression analysis and summary statistics are given below. A 99% confidence interval for the mean lawn quality of all lawns sown with a seed density of 2.9 was found to be (32.3, 56.3). Give an interpretation of this interval. 30) Variable Count Mean StdDev Range Seed Density 8 2.75 0.49099 4 Lawn Quality 8 45.625 3.712611 35 Dependent variable is: Lawn Quality R-squared = 36.0% s = 9.073602 with 8-2 = 6 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Constant 33.14815 7.510757 4.413423 0.004503 Seed Density 4.537037 2.469522 1.837213 0.115825 A) Based on this regression, we are 99% confident that the average seed density will increase between 32.3 and 56.3 pounds per 500 square feet for each additional one-point increase in lawn quality. B) Based on this regression, 99% of all random samples will have an average lawn quality between 32.3 and 56.3. C) Based on this regression, we are 99% confident that the average lawn quality for lawns with a seed density of 2.9 pounds per 500 square feet is between 32.3 and 56.3. D) Based on this regression, we are 99% confident that the lawn quality for a lawn with a seed density of 2.9 is between 32.3 and 56.3. E) Based on this regression, we are 99% confident that the average lawn quality will increase between 32.3 and 56.3 points for each additional pound of seed per 500 square feet. Provide an appropriate response. 31) A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight similar plots of land are selected and each is planted with a particular density of seed. One month later the quality of each lawn is rated on a scale of 0 to 100. The regression analysis is given below. Given a 95% confidence interval, Is there evidence of an association between seed density and lawn quality? 31) Dependent variable is: Lawn Quality R-squared = 36.0% s = 9.073602 with 8-2 = 6 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Constant 33.14815 7.510757 4.413423 0.004503 Seed Density 4.537037 2.469522 1.837213 0.115825 12