Chapter 4 Exam. A scatterplot of a response variable Y versus an explanatory variable X is given below.
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1 Chapter 4 Exam A scatterplot of a response variable Y versus an explanatory variable X is given below. 1 Which of the following is true? A) There is a nonlinear relationship between Y and X. B) There is a very strong positive correlation between Y and X because there is an obvious relationship between these variables. C) There is a monotonic relationship between Y and X. D) There is a strong quadratic relationship between Y and X Suppose we measure a response variable Y at each of several times. A scatterplot of log Y versus time of measurement looks approximately like a positively sloping straight line. We may conclude that A) the correlation between time of measurement and Y is negative, since logarithms of positive fractions (such as correlations) are negative. B) the rate of growth of Y is positive, but slowing down over time. C) a logarithmic growth model would approximately describe the relationship between Y and the time of measurement. D) a mistake has been made. It would have been better to plot Y versus the logarithm of the time of measurement. E) an exponential growth model would approximately describe the relationship between Y and time of measurement. Suppose the relationship between a response variable y and a predictor variable x is approximately y = x Which of the following plots would approximately follow a straight line? A) A plot of y against x. D) A plot of 10 y against x. B) A plot of y against log x. E) A plot of log y against log x. C) A plot of log y against x. When possible, the best way to establish that an observed association is the result of a cause-and-effect relation is by means of A) the least-squares regression line. B) the correlation coefficient. C) randomization to select the data variables. D) a well-designed experiment. E) examining z-scores rather than the original variables.
2 Which of the following scatterplots would indicate that Y is growing exponentially over time? A) C) B) D) 5 E) 6 The owner of a chain of supermarkets notices that there is a positive correlation between the sales of beer and the sales of ice cream over the course of the previous year. During seasons when sales of beer were above average, sales of ice cream also tended to be above average. Likewise, during seasons when sales of beer were below average, sales of ice cream also tended to be below average. Which of the following would be a valid conclusion from these facts? A) The sales records must be in error. There should be no association between beer and ice cream sales. B) Temperature is clearly a lurking variable when considering sales of beer and ice cream. C) A scatterplot of monthly ice cream sales versus monthly beer sales would show that a straight line describes the pattern in the plot, but it would have to be a horizontal line. D) Evidently, for a significant proportion of customers of these supermarkets, drinking beer causes a desire for ice cream or eating ice cream causes a thirst for beer. E) None of the above.
3 7 Two variables, an explanatory variable x and a response variable y, are measured on each of several individuals. The correlation between these variables is found to be To help us interpret this correlation, we should do which of the following? A) Compute the least-squares regression line of y on x and consider whether the slope is positive or negative. B) Interchange the roles of x and y (i.e., treat x as the response variable and y as the explanatory variable) and recompute the correlation. C) Plot the data. D) Determine whether x or y has larger values before computing the residuals. 8 According to the 1990 census, those states that had an above-average number X of people who failed to complete high school tended to have an above-average number Y of infant deaths. In other words, there was a positive association between X and Y. The most plausible explanation for this association is that A) populations were used instead of rates. B) Y causes X. Therefore, programs that reduce infant deaths will ultimately reduce the number of high school dropouts. C) changes in X and Y are due to a common response to other variables. For example, states with large populations will have both larger numbers of people who fail to complete high school and larger numbers of infant deaths. D) the association between X and Y is purely coincidental. It is implausible to believe the observed association could be anything other than accidental. E) X causes Y. Therefore, programs to keep teens in school will help reduce the number of infant deaths Which of the following would be necessary to establish a cause-and-effect relation between two variables? A) Strong association between the variables. B) A well-designed experiment. C) Plausibility of the alleged cause. D) An association between the variables observed in many different settings A researcher notices that in a sample of adults, those that take larger amounts of vitamin C have fewer illnesses. However, those that take larger amounts of vitamin C also tend to exercise more. As explanations for having fewer illnesses, the variables amount of vitamin C taken and amount of exercise are A) skewed. B) confounded. C) common responses. D) symmetric. E) linked.
4 In 1982 Kennesaw, Georgia, passed a law requiring all citizens to own at least one gun. Although the law was never enforced, six months after the law was passed the number of burglaries in that month was less than in the month prior to passage of the law. We may conclude which of the following? A) Gun ownership and burglary rates are negatively associated. B) Gun ownership causes a reduction in crime. This is because there is a negative association between gun ownership and burglary rates and because there is a plausible explanation for this association (gun ownership acts as a deterrent to crime). C) Criminals are more likely to avoid homes in towns where guns are more prevalent. D) All of the above. E) None of the above. 33. The reversal of the direction of an association when lurking variables are taken into account is called A) Simpson s paradox. D) a residual plot. B) least-squares regression. E) negative association. C) confounding. 34. The two-way table below categorizes suicides committed in 1983 by the sex of the victim and the method used. Method Male Female Firearms 13,959 2,641 Poison 3,148 2,469 Hanging 3, Other 1, Which of the following statements is consistent with the table? A) There is absolutely no evidence of a relation between the sex of the victim and the method of suicide used. B) More women commit suicide than men. C) Men display a greater tendency to use firearms to commit suicide than do women. D) The correlation between method of suicide and sex of the victim is clearly positive. E) The proportion of men who use poison to commit suicide is higher than the proportion of women who use poison to commit suicide. 36. X and Y are two categorical variables. The best way to determine whether there is a relationship between them is to A) compute the least-squares regression line between X and Y. B) draw a scatterplot of the X and Y values. C) make a two-way table of the X and Y values. D) calculate the correlation between X and Y. E) do all of the above.
5 Researchers studied a sample of 100 adults between the ages of 25 and 35 and found a strong negative correlation between the amount of vitamin C an individual consumed and the number of pounds the individual was overweight. Which of the following may we conclude? A) This is strong, but not conclusive, evidence that large amounts of vitamin C inhibit weight gain. B) If the amount of vitamin C consumed and the number of pounds overweight for each individual in this study were plotted on a scatterplot, the points would lie close to a negatively sloping straight line. C) If a larger sample of adults between the ages of 25 and 35 had been studied, the correlation would have been even stronger. D) If people consumed more vitamin C, they would likely lose more weight. FREE RESPONSE 16. What does the dotted line represent in the figure below? X Y 17. Over the past 30 years in the United States there has been a strong positive correlation between cigarette sales and the number of high school graduates. Is the association between these two variables most likely due to causation, confounding, or common response? Justify your answer 18. If someone suspects a relationship between two quantitative variables to follow the equation y = ax 2, what transformation could be performed without using logarithms to achieve linearity?
6 19. A company decided to expand, so it opened a new factory with 455 available jobs. The following tables summarize the hiring decisions made by the company. Workers Managers Male Female Male Female Applied Applied Hired Hired (a) Calculate the percent of male and female workers that are hired. Then do likewise for male and female managers. (b) Use the tables above to create a two-way table that shows the relationship between gender and hiring decision. (c) Calculate the percent of male and female applicants that were hired. (d) Explain your findings in (a) and (c). (explain why it is happening not just what it is)
7 20. Cell phones, a fairly recent innovation, have become increasingly popular with all segments of our society. According to the Strategis Group, the number of cellular and personal communications systems subscribers in the United States increased dramatically beginning in 1990, as shown in the following table. No. of subscribers Year (millions) (a) Describe the relationship between year and number of subscribers. (b) What type of relationship appears to be present? Justify your answer. (c) Perform an appropriate transformation to linearize the data. Find the equation of the leastsquares line for the transformed data. Write the equation below. Be sure to define any variables you use. (d) How well does the linear model you calculated in (c) fit the transformed data? Justify your answer with graphical and numerical evidence. (e) The Strategis Group predicts 70.8 million subscribers in 1998, and 99.2 million in the year How many subscribers does your model predict for these years? Show your method.
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