Average Longevity (years) Gestation (days)

Transcription

1 AP Statistics Review Chapters 9-10 Practice Problems Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question. 1) The scatterplot below displays the average longevity (in years) plotted against gestation (in days) for a number of different mammals. For what range of gestation lengths is a linear model appropriate? 1) 24 y Average Longevity (years) Gestation (days) A) One linear model for 0 through 100 days and another linear model for 150 through 350 days. B) A linear model should be used for each pair of adjacent data points. C)A single linear model is appropriate for the entire data set. D) One linear model for 0 through 200 days and another linear model for 200 through 350 days. E) A linear model should not be used for any part of the data. 1

2 Solve the problem. 2) The figure below shows the recent trend in first-birth rate for American women between the ages of 18 and 19. (The first-birth rate is the number of 18 to 19 year-olds per 1000 who give birth to their first child). 2) The regression analysis of this data yields the following values: Variable Coefficient Constant Year R2 = Use this model to predict the first-birth rate for 18 to 19 year-olds in A) 51 per 1000 B) 56 per 1000 C)49 per 1000 D) 59 per 1000 E) 53 per

3 Answer the question. 3) The figure below examines the association between life expectancy and computer ownership for several countries. Also shown are the equation and R2 value from a linear regression analysis. What is the best conclusion to draw from the figure? 3) A) Although the association is strong, computer ownership probably does not promote longevity. Instead, national per capita wealth is probably a lurking variable that drives both life expectancy and computer ownership. B) Persons who live longer buy more computers over the course of their longer lifetimes. C) Exposure to the radiation from computer monitors is causing a clear decline in life expectancy. D) Clearly, there must be some as-yet unknown health benefit associated with using computers. E) Computer ownership promotes health and long life, probably due to the greater access that computer owners have to health information on the world-wide web. 4) A study of consumer behavior finds a strong positive association between sales of ice cream and sales of soda. Describe three different possible cause-and-effect relationships that might be present. A) Perhaps sales of ice cream cause higher sales of soda, sales of soda cause higher sales of ice cream, or both could be caused by a lurking variable such as the outdoor temperature. B) There is only one cause-and-effect relationship: sales of ice cream cause higher sales of soda. C) There is only one cause-and-effect relationship: sales of soda cause higher sales of ice cream. D) There are only two cause-and-effect relationships: sales of ice cream cause higher sales of soda, or sales of soda cause higher sales of ice cream. E) There are no possible cause-and-effect relationship, because there should be an arithmetic mistake. 4) 5) Which of the following scatterplots of residuals suggests that a linear model may not be applicable? 5) I II 3

4 III IV A) III B) IV C)I D) II E) None of the above 4

5 6) If the point in the upper right corner of this scatterplot is removed from the data set, then what will happen to the slope of the line of best fit (b) and to the correlation (r)? 6) A) b will increase, and r will decrease. B) both will increase. C)both will remain the same. D) b will decrease, and r will increase. E) both will decrease. Solve the problem. 7) For the model y^ = x, predict y when x = 2. Round to two decimal places. A) 0.00 B) C) D) 8.25 E) ) 8) For the model y^ = x, predict y when x = 2. Round to two decimal places. A) B) C) 2.55 D) E) 6.5 8) 5

6 Provide an appropriate response. 9) One of the important factors determining a car's fuel efficiency is its weight. This relationship is examined for 11 cars, and the association is shown in the scatterplot below. 9) Fuel Efficiency (mpg) Weight (1000 lbs) If a linear model is considered, the regression analysis is as follows: Dependent variable: MPG R-squared = 84.7% VARIABLE COEFFICIENT Intercept Weight What does the slope say about this relationship? A) Gas mileage decreases an average of mpg for each thousand pounds of weight. B) Gas mileage decreases an average of mpg for each thousand pounds of weight. C)Gas mileage increases an average of mpg for each thousand pounds of weight. D) Gas mileage increases an average of mpg for each thousand pounds of weight. E) Gas mileage decreases an average of.7346 mpg for each thousand pounds of weight. 6

7 10) The relationship between two quantities x and y is examined, and the association is shown in the scatterplot below. 10) 44 y x Describe the association between these variables shown in the scatterplot. A) Fairly linear, weak relationship B) Fairly linear, strong relationship C) Fairly quadratic, weak relationship D) Fairly exponential, weak relationship E) Fairly exponential, strong relationship Create an appropriate model for the data. 11) Consider the data listed in the following table. 11) X Y Create an appropriate model. Estimate the value of y when x = 27. Round your answer to four decimal places. A) B) C) D) E)

8 Solve the problem. 12) The consumer price index (CPI) is a measure of the relative cost of goods in the a given country for a particular year. The table below shows the CPI for a country for the stated years beginning in ) Year CPI Create an appropriate model to re-express the CPI. What re-expression of the CPI does this model involve? A) B) log (CPI) C) D) CPI E) - CPI log (CPI) CPI Provide an appropriate response. 13) A company's sales increase by the same amount each year. This growth is... A) power B) exponential C) linear D) logarithmic E) quadratic 13) 14) Which statement about re-expressing data is not true? I. Unimodal distributions that are skewed to the left will be made more symmetric by taking the square root of the variable. II. A curve that is descending as the explanatory variable increases may be straightened by looking at the reciprocal of the response variable. III. One goal of re-expression may be to make the variability of the response variable more uniform. A) I only B) II and III C)I, II, and III D) III only E) II only 14) 8

9 Answer Key Testname: CHAPTERS 9-10 REVIEW 1) A 2) E 3) A 4) A 5) D 6) D 7) D 8) B 9) B 10) E 11) B 12) B 13) C 14) B 9