Sem. 1 Review Ch. 1-3

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1 AP Stats Sem. 1 Review Ch. 1-3 Name 1. You measure the age, marital status and earned income of an SRS of 1463 women. The number and type of variables you have measured is a. 1463; all quantitative. b. four; two categorical and two quantitative. c. four; one categorical and three quantitative. d. three; two categorical and one quantitative. e. three; one categorical and two quantitative. 2. Consumers Union measured the gas mileage in miles per gallon of model automobiles on a special test track. The pie chart below provides information about the country of manufacture of the model cars used by Consumers Union. Based on the pie chart, we may conclude that: a. Japanese cars get significantly lower gas mileage than cars of other countries. This is because their slice of the pie is at the bottom of the chart. b. U.S cars get significantly higher gas mileage than cars from other countries. c. Swedish cars get gas mileages that are between those of Japanese and U.S. cars. d. Mercedes, Audi, Porsche, and BMW represent approximately a quarter of the cars tested. e. More than half of the cars in the study were from the United States. 3. Normal body temperature varies by time of day. A series of readings was taken of the body temperature of a subject. The mean reading was found to be 36.5 C with a standard deviation of 0.3 C (recall that F = C(1.8) + 32). When converted to F, the mean and standard deviation are: a. 97.7, 32 b. 97.7, 0.30 c. 97.7, 0.54 d. 97.7, 0.97 e. 97.7, Which of the following is likely to have a mean that is smaller than the median? a. The salaries of all National Football League players. b. The scores of students (out of 100 points) on a very easy exam in which most get nearly perfect scores but a few do very poorly. c. The prices of homes in a large city. d. The scores of students (out of 100 points) on a very difficult exam in which most get poor scores but a few do very well. e. Amounts awarded by civil court juries. 5. The weights of the male and female students in a class are summarized in the following boxplots: Which of the following is NOT correct?

2 a. About 50% of the male students have weights between 150 and 185 pounds. b. About 25% of female students have weights more than 130 pounds. c. The median weight of male students is about 162 pounds. d. The mean weight of female students is about 120 pounds because of symmetry. e. The male students have less variability than the female students. 6. For the following histogram, what is the proper ordering of the mean, median, and mode? Note that the graph is NOT numerically precise only the relative positions are important. a. I = mean, II = median, III = mode b. I = mode, II = median, III = mean c. I = median, II = mean, III = mode d. I = mode, II = mean, III = median e. I = mean, II = mode, III = median 7. A medical researcher collects health data on many women in each of several countries. One of the variables measured for each woman in the study is her weight in pounds. The following list gives the five-number summary for the weights of women in one of the countries. Country A: 100, 110, 120, 160, 200 About what percentage of Country A women weigh between 110 and 200 pounds? a. 50% b. 65% c. 75% d. 85% e. 95% 8. The following bar graph gives the percent of owners of three brands of trucks who are satisfied with their truck. From this graph we may legitimately conclude that: a. Owners of other brands of trucks are less satisfied than the owners of these three brands. b. Chevrolet owners are substantially more satisfied than Ford or Toyota owners. c. There is very little difference in the satisfaction of owners for the three brands. d. Chevrolet probably sells more trucks than Ford or Toyota. e. A pie chart would have been a better choice for displaying this data. 9. A sample of 99 distances has a mean of 24 feet and a median of 24.5 feet. Unfortunately, it has just been discovered that an observation which was erroneously recorded as 30 actually had a value of 35. If we make this correction to the data, then: a. The mean remains the same, but the median is increased. b. The mean and median remain the same. c. The median remains the same, but the mean is increased. d. The mean and median are both increased. e. We do not know how the mean and median are affected without further calculations, but the variance is increased.

3 10. The five-number summary for scores on a statistics exam is 11, 35, 61, 70, 79. In all, 380 students took the test. About how many had scores between 35 and 61? a. 26 b. 76 c. 95 d. 190 e. None of these 11. The heights of American men aged 18 to 24 are approximately normally distributed with mean 68 inches and standard deviation 2.5 inches. Only about 5% of young men have heights outside the range a inches to 70.5 inches b. 63 inches to 73 inches c inches to 75.5 inches d. 58 inches to 78 inches e. none of the above 12. For the density curve shown below, which statement is true? a. The density curve is symmetric. b. The density curve is skewed right. c. The area under the curve between 0 and 1 is 1. d. The density curve is normal. is correct. 13. For the density curve shown below, which statement is true? a. The mean and median are equal. b. The mean is greater than the median. c. The mean is less than the median. d. The mean could be either greater than or less than the median. e. None is the above is correct. 14. The area under the standard normal curve corresponding to 0.3<Z<1.6 is a b c d Suppose that sixteen-ounce bags of chocolate chips cookies are produced with an actual mean weight of 16.1 ounces and a standard deviation of 0.1 ounce. The percentage of bags that will contain between 16.0 and 16.1 ounces is a. 10 b. 16 c. 34 d. 68 e. none of the above

4 16. A company produces packets of soap powder labeled "Giant Size 32 Ounces." The actual weight of soap powder in a box has a normal distribution with a mean of 33 oz. and a standard deviation of 0.8 oz. What proportion of packets are underweight (i.e., weigh less than 32 oz.)? a b c d e For the density curve below, what percent of the observations lie between 0.5 and 1.2? a. 25% b. 35% c. 50% d. 68% e. 70% 18. If the heights of 99.7% of American men are between 5'0" and 7'0", what is your estimate of the standard deviation of the height of American men? a. 1 b. 3 c. 4 d. 6 e Suppose that the distribution of math SAT scores from your state this year is normally distributed with mean 480 and standard deviation 100 for males, and mean 440 and standard deviation 120 for females. If someone who scores 780 or higher on math SAT can be considered a genius, what is the proportion of geniuses among the male SAT takers? a. 26% b. 13% c. 3% d. 1.3% e. 0.13% 20. The average yearly snowfall in Chillyville is normally distributed with a mean of 55 inches. If the snowfall in Chillyville exceeds 60 inches in 15% of the years, what is the standard deviation? a inches b inches c inches d inches e. The standard deviation cannot be computed from the given information. 21. In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. The equation was y = x where y is the final exam score and x is the score on the first test. Carla scored 95 on the first test. On the final exam, Carla scored 98. What is the value of her residual? a. 98 b. 2.5 c. 2.5 d. 0

5 22. In the scatterplot below, if each x-value were decreased by one unit and the y-values remained the same, then the correlation r would a. Decrease by 1 unit b. Decease slightly c. Increase slightly d. Stay the same e. Can t tell without knowing the data values 23. In regression, the residuals are which of the following? a. Those factors unexplained by the data b. The difference between the observed responses and the values predicted by the regression line c. Those data points which were recorded after the formal investigation was completed d. Possible models unexplored by the investigator 24. Which of the following statements are true? I. Correlation and regression require explanatory and response variables. II. Scatterplots require that both variables be quantitative. III. Every least-square regression line passes through (x, y). a. I and II only b. I and III only c. II and III only d. I, II, and III 25. Suppose the following information was collected, where X = diameter of tree trunk in inches, and Y = tree height in feet. X Y If the LSRL equation is y = x, what is your estimate of the average height of all trees having a trunk diameter of 7 inches? a b c d e Suppose we fit the least squares regression line to a set of data. What is true if a plot of the residuals shows a curved pattern? a. A straight line is not a good model for the data. b. The correlation must be 0. c. The correlation must be positive. d. Outliers must be present. e. The LSRL might or might not be a good model for the data, depending on the extent of the curve.

6 27. Which of the following are resistant? a. Least squares regression line b. Correlation coefficient c. Both the least squares line and the correlation coefficient d. Neither the least squares line nor the correlation coefficient e. It depends 28. A copy machine dealer has data on the number x of copy machines at each of 89 customer locations and the number y of service calls in a month at each location. Summary calculations give x= 8.4, S x = 2.1, y= 14.2, S y = 3.8, and r = What is the slope of the least squares regression line of number of service calls on number of copiers? a b c d. None of these e. Can t tell from the information given 29. There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least squares fit of some data collected by a biologist gives the model y= x, 9 < x < 25, where x is the number of chirps per minute and y is the estimated temperature in degrees Fahrenheit. What is the estimated increase in temperature that corresponds to an increase in 5 chirps per minute? a. 3.3 F b F c F d F e F 30. A set of data relates the amount of annual salary raise and the performance rating. The least squares regression equation is y = 1, ,000x where y is the estimated raise and x is the performance rating. Which of the following statements is not correct? a. For each increase of one point in performance rating, the raise will increase on average by $2,000. b. This equation produces predicted raises with an average error of 0. c. A rating of 0 will yield a predicted raise of $1,400. d. The correlation for the data is positive. e. All of the above are true.