AP Statistics Semester Exam Review Chapters 1-3

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1 AP Statistics Semester Exam Review Chapters Here are the IQ test scores of 10 randomly chosen fifth-grade students: To make a stemplot of these scores, you would use as stems (a) 0 and 1. (b) 09, 10, 11, 12, 13, and 14. (c) 96, 110, 118, 122, 125, 126, 130, 139, and 145. (d) 0, 2, 3, 5, 6, 8, 9. (e) None of the above is a correct answer. 2. For the IQ test scores from the previous question, what kind of plot is appropriate? (a) a stemplot but not a boxplot (b) a boxplot but not a histogram (c) a bar graph but not a pie chart (d) a histogram but not a dotplot (e) None of the above is a correct answer. 3. Rainwater was collected in water collectors at 30 different sites near an industrial complex and the amount of acidity (ph level) was measured. The data ranged from ph 2.6 to ph 6.3. The following stemplot of the data was constructed Which of the following boxplots is correct? 4. A scientist is weighing each of 30 fish. She obtains a mean of 30 g and a standard deviation of 2 g. After completing the weighing, she finds that the scale was misaligned and always under reported every weight by 2 g that is, a fish that really weighed 26 g was reported to weigh 24 grams. What are the mean and standard deviation after correcting for the error in the scale? (a) 28 g, 2 g (b) 30 g, 4 g (c) 32 g, 2 g (d) 32 g, 4 g (e) 28 g, 4 g

2 5. A smooth curve which approximates the shape of a histogram and describes the overall pattern of a distribution is called (a) a stemplot (b) a Normal probability plot (c) a destiny curve (d) a density curve (e) none of the above 6. The following graph is a Normal probability plot for the amount of rainfall (in acrefeet) obtained from 26 randomly selected clouds that were seeded with silver oxide. Which of the following statements about the shape of the rainfall distribution is true? (a) The distribution is Normal. (b) The distribution is approximately Normal. (c) The distribution is roughly symmetric. (d) The distribution has no potential outliers. (e) The distribution is skewed. 7. The distribution of the heights of students in a large class is roughly Normal. Moreover, the average height is 68 inches, and approximately 95% of the heights are between 62 and 74 inches. Thus, the standard deviation of the height distribution is approximately equal to (a) 2 (b) 3 (c) 6 (d) 9 (e) If a store runs out of advertised material during a sale, customers become upset, and the store loses not only the sale but also goodwill. From past experience, a music store finds that the mean number of CDs sold in a sale is 845, the variance is 225, and a histogram of the demand is approximately Normal. The manager is willing to accept a 2.5% chance that a CD will be sold out. About how many CDs should the manager order for an upcoming sale? (a) 1295 (b) 1070 (c) 935 (d) 875 (e) 860

3 9. For children between the ages of 18 months and 29 months, there is approximately a linear relationship between height and age. The relationship can be represented by ŷ = x, where y represents height (in centimeters) and x represents age (in months). Joseph is 22.5 months old and is 80 centimeters tall. What is Joseph's residual? ` (a) 79.1 (b)! 0.9 (c) 0.9 (d) 56.6 (e) A study examined the relationship between the sepal length and sepal width for two varieties of an exotic tropical plant. Varieties A and B are represented by x s and o s, respectively, in the following scatterplot. Which of the following statements is FALSE? (a) Considering Variety A only, there is a negative correlation between sepal length and width. (b) Considering Variety B only, the least-squares regression line for predicting sepal length from sepal width has a negative slope. (c) Considering both varieties, there is a positive correlation between sepal length and width. (d) Considering each variety separately, there is a positive correlation between sepal length and width. (e) Considering both varieties, the least-squares regression line for predicting sepal length from sepal width has a positive slope. 11. On May 11, 50 randomly selected subjects had their systolic blood pressure (SBP) recorded twice the first time at about 9:00 a.m. and the second time at about 2:00 p.m. If one were to examine the relationship between the morning and afternoon readings, then one might expect the correlation to be (a) near zero, as morning and afternoon readings should be independent. (b) high and positive, as those with relatively high readings in the morning will tend to have relatively high readings in the afternoon. (c) high and negative, as those with relatively high readings in the morning will tend to have relatively low readings in the afternoon. (d) near zero, as correlation measures the strength of the linear association. (e) near zero, as blood pressure readings should follow approximately a Normal distribution. 12. Suppose we fit a 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 regression line might or might not be a good model for the data, depending on the extent of the curve.

4 13. Here are data on the percent of people in several age groups who attended a movie in the past 12 months: Age group Movie attendance 18 to 24 years 83% 25 to 34 years 73% 35 to 44 years 68% 45 to 54 years 60% 55 to 64 years 47% 65 to 74 years 32% 75 years and over 20% (a) Display these data in a bar graph in the space above. What is the main feature of the data? (b) Would it be correct to make a pie chart of these data? Why? (c) A movie studio wants to know what percent of the total audience for movies is 18 to 24 years old. Explain why these data do not answer this question. 14. The distance between two mounting holes is important to the performance of an electrical meter. The manufacturer measures this distance regularly for quality control purposes, recording the data as thousandths of an inch more than inches. For example, is recorded as 44. The figure below is a Normal probability plot of the distances for the last 90 electrical meters measured. (a) Is the overall shape of the distribution roughly Normal? Justify your answer. (b) Why does the plot have a stair-step appearance?

5 Because elderly people may have difficulty standing to have their heights measured, a study looked at predicting overall height from height to the knee. Here are data (in centimeters) for five elderly men: K knee height x Height y Construct a scatterplot on your calculator. Describe the form, direction, and strength of the relationship that you see. 16. Use your calculator to determine the least-squares regression line. Write the equation below. Be sure to define any variables you use. 17. Interpret the slope of the regression line in the context of the problem. 18. Interpret the value of 2 r in the context of the problem. 19. We define the standard deviation of the residuals, s, by and interpret its value in the context of the problem. s = residuals 2 ". Calculate s n! Should you use your regression line from Question 10 to predict the height of an elderly man whose knee height is 70 centimeters? If so, do it. If not, explain why not.

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