SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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1 Suggested Review Problems - Chapter Inference for Slope/Regression and Slope Intervals Name Date : 2/19/2015 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Decide whether or not the conditions and assumptions for regression inference are satisfied. Explain your answer. 1) Ten students from a large lecture course were randomly sampled to see how many hours 1) they studied for the final exam and their grade on the final exam. The professor wants to conduct a linear regression to determine if there is an association between the amount of time spent studying and the student's grade on the exam. Several plots are shown below. 1

2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the given regression analysis to find and interpret the equation of the regression line. 2) Applicants for a particular job, which involves extensive travel in Spanish-speaking countries, must take a proficiency test in Spanish. The sample data were obtained in a study of the relationship between the numbers of years applicants have studied Spanish and their score on the test. 2) R-squared = 83.0% A) Score = Number of Years; The scores on the proficiency test for these applicants increase about points for each additional year spent studying Spanish. B) Score = Number of Years ; The scores on the proficiency test for these applicants increase about points for each additional year spent studying Spanish. C) Number of Years = Score; The number of years spent studying Spanish increases about years for each additional point scored on the test. D) Score = Number of Years; The scores on the proficiency test for these applicants increase about points for each additional year spent studying Spanish. E) Score = Number of Years ; The scores on the proficiency test for these applicants increase about points for each additional year spent studying Spanish. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Perform the required t-test for the slope of the regression line and state your conclusion. 3) Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The following data consist of the students' GPAs on entering the program and their current GPAs. 3) Entering GPA Current GPA At the 10% level of significance, do the data provide sufficient evidence to conclude that entering GPA is useful as a predictor of current GPA? 2

3 Provide an appropriate response. 4) Applicants for a particular job, which involves extensive travel in Spanish-speaking countries, must take a proficiency test in Spanish. The sample data below were obtained in a study of the relationship between the numbers of years applicants have studied Spanish and their score on the test. Given a 95% confidence interval, Do the data provide sufficient evidence to conclude that the slope of the regression line is not 0 and hence that number of years of study is useful as a predictor of score on the test? The regression analysis is given below. 4) R-squared = 83.0% 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. 5) Applicants for a particular job, which involves extensive travel in Spanish-speaking countries, 5) must take a proficiency test in Spanish. The sample data were obtained in a study of the relationship between the numbers of years applicants have studied Spanish and their score on the test. Use the regression analysis given below to find a 99% confidence interval for the slope of the regression line. R-squared = 83.0% A) (25.70, 37.40) B) (6.88, 14.93) C) (5.23, 16.57) D) (9.16, 12.65) E) (5.05, 16.76) 3

4 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 6) Applicants for a particular job, which involves extensive travel in Spanish-speaking countries, must take a proficiency test in Spanish. The sample data below were obtained in a study of the relationship between the numbers of years applicants have studied Spanish and their score on the test. Use the regression analysis below to explain what the R-squared in this regression means. 6) R squared = 83.0% MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 7) Several volunteers engage in a special exercise program intended to lower their blood pressure. We measure each person's initial blood pressure, lead them through the exercises daily for a month, then check blood pressures again. Suppose that after the study we want to see if there's evidence that an exercise program's effectiveness in lowering blood pressure depends on how high the person's initial blood pressure was. We should do a A) χ 2 test of homogeneity B) matched pairs t-test C) 2-sample t-test D) χ 2 goodness-of-fit test E) linear regression t-test 7) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Suppose you were asked to analyze each of the situations described below. (NOTE: DO NOT DO THESE PROBLEMS!) For each, indicate which inference procedure you would use (from the list), the test statistic (z, t, or χ 2 ), and, if t or χ 2, the number of degrees of freedom. proportion, 1 sample difference of proportions, 2 samples mean, 1 sample mean of differences, matched pairs difference of means, independent samples goodness of fit homogeneity independence regression, inference for β 8) Researchers offer small cookies to nine nursery school children and record the number of cookies consumed by each. Forty-five minutes later they observe these children during recess, and rate each child for hyperactivity on a scale from Is there any evidence that sugar contributes to hyperactivity in children? 8) 4

5 9) The Comprehensive Test of Basic Skills (CTBS) is used by school district to assess student progress. Two of the areas tested are math and reading. A random sample of student results was reviewed to determine if there is an association between math and reading scores on the CTBS. Here are the scatterplot, the residuals plot, a histogram of the residuals, and the regression analysis of the data. Use this information to analyze the association between the math and reading scores on the CTBS. 9) What do you conclude? 5

6 Suppose you were asked to analyze each of the situations described below. (NOTE: DO NOT DO THESE PROBLEMS!) For each, indicate which inference procedure you would use (from the list), the test statistic (z, t, or χ 2 ), and, if t or χ 2, the number of degrees of freedom. proportion, 1 sample difference of proportions, 2 samples mean, 1 sample mean of differences, matched pairs difference of means, independent samples goodness of fit homogeneity independence regression, inference for β 10) A researcher wonders if meat in the diet may be a factor in high blood pressure. She compares the blood pressures of 40 randomly selected vegetarians, to those of 40 people who eat meat. 10) 6

7 Answer Key Testname: UNTITLED1 1) Answers will vary. Possible answer: The scatterplot shows a strong linear relationship between hours spent studying and exam scores, which verifies the linearity assumption. The plot of residuals against predicted values has no obvious pattern, and the spread around the x-axis is fairly constant. This confirms the equal variance assumption. The histogram of the residuals is unimodal and reasonably symmetric. The normality assumption seems plausible, especially since the sample size is small. Overall, the assumptions for regression inference appear to be satisfied. 2) A 3) H0: β1 = 0 HA: β1 0 Test statistic t = P-value = Do not reject H0. At the 10% level of significance, the data do not provide sufficient evidence to conclude that the slope of the population regression line is different from 0 and hence that entering GPA is useful as a predictor of current GPA. 4) H0: No linear relationship between the number of years and test score, β1 = 0. HA: There is a linear relationship between the number of years and test score, β1 0. t = 6.25 P-value = Reject H0. With the small P-value, the data provide sufficient evidence to conclude that the slope of the regression line is not 0 and hence that there is strong evidence of a linear relationship between years of study and score on the test. 5) E 6) 83% of the variation in test scores is accounted for by the regression on the number of years applicants have studied Spanish. 7) E 8) regression, inference for β; t; 9 degrees of freedom 9) The P-value is very small, so we reject the null hypothesis. There is strong evidence of a positive association between CTBS scores Math and Reading. 10) difference of means, independent samples; t; 39 degrees of freedom 7

ch12 practice test SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

ch12 practice test SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. ch12 practice test 1) The null hypothesis that x and y are is H0: = 0. 1) 2) When a two-sided significance test about a population slope has a P-value below 0.05, the 95% confidence interval for A) does