You have 70 minutes to answer these 32 multiple choice statistics questions. At the end of the test you may compare your results with those of other website visitors. Advanced Placement is a registered trademark of the College Board, which was not involved in the production of, and does not endorse this web site. Question 1: What is the value m in the table below, if the mean and the variance of the random variable X are μ_{x} = 25 and σ^{2}_{x} = 80? X10203035m Probability.1.5.1.2.1 m = 30 m = 35 m = 38 m = 40 m = 45 Question 2: Two distributions D_{1} and D_{2} are displayed on the same graph. If the distribution D_{1} is right skewed, the distribution D_{2} is left skewed, and the mean of D_{1} is lower than the mean of D_{2}, which of the following statements is not true? The median of D_{1} is lower than the median of D_{2} The mean of D_{1} is lower than the median of D_{2}. The mean of D_{2} is lower than the median of D_{1}. The median of D_{1} is lower than the mean of D_{2}. The mean of D_{2} is lower than the median of D_{2}. Question 3: A large sample of size n is used to estimate the confidence interval for a proportion p. After further evaluation, the standard deviation of the sample distribution is considered too large. What size sample do we need to use for a new standard error equal to one tenth of the original standard error? 10n 50n 100n 141n 200n Question 4: A box contains 3 yellow, 2 red, 4 green and 3 black marbles. Two marbles are taken one after the other at random from the box. What is the probability that both marbles are red? 1/50 1/60 1/66 1/24 1/18 Question 5: A large automobile manufacturer states that approximately 4% of all their cars made in 2010 have a defective component. Two samples of 150 cars (sample A) and 250 cars (sample B) were taken to test for the defective component. Which of the following statements must be true: mean of sample A < mean of sample B mean of the sample A > mean of sample B standard deviation of sample A = standard deviation of sample B standard deviation of sample A < standard deviation of sample B standard deviation of sample A > standard deviation of sample B Question 6: You roll a die until you get a 5 or a 6. What is the variance of this distribution? 6 3 1/3 8 12 Question 7: A back to back stem and leaf plot compares the heights of the players of two basketball teams. All heights in the plot below are in inches. Team A Team B 68 9 1 4 4 4 5 8 972 3 6 6 6 8 9 1 1 2 482 5 6 The means of the two distributions are the same. The medians of the two distributions are the same. The ranges of the two distributions are the same. The distributions have the same number of observations. None of the statements above is correct. Question 8: A car manufacturer wishes to estimate the difference in early failures between cars sold in a warm climate and cars sold in a cold climate. They take a random sample of 500 cars from each group. The means obtained are 4.1 failures for cars running in a warm climate and 3.8 failures for cars running in a cold climate. The standard deviation for both populations is 0.4 failures. Find the 95% confidence interval for the difference in the population means. 0.3 +/- 0.0333 0.3 +/- 0.0350 0.3 +/- 0.0400 0.3 +/- 0.0452 0.3 +/- 0.0496 Question 9: A nutritional consulting company is trying to find what percentage of the population of a town is overweight. The marketing department of the company contacts by telephone 600 people from a list of the entire town's population. All 100 people give answers to the survey. Which of the following is the most significant source of bias in this survey? Size of sample. Undercoverage. Voluntary response bias Nonresponse. Response bias. Question 10: Which of the following are true statements: I. All bell-shaped distributions are symmetric. II. Bar charts are useful to describe quantitative data. III. Cumulative frequency plots are useful to describe quantitative data. I only. I and II only. II and III only. I and III only. I, II and III. Question 11: A random sample of 400 passengers of an airline is polled after their flights. Of the passengers, 300 say they will fly again with the same airline. Which of the following is a 90% confidence interval for the proportion of passengers that will fly again with the same airline? 0.75 +/- 0.066 0.75 +/- 0.005 0.75 +/- 0.045 0.75 +/- 0.036 0.75 +/- 0.15 Question 12: The mean number of points per game scored by basketball players during a high school championship is 9.4, and the standard deviation is 1.5. Assuming that the number of points are normally distributed, what number of points per game will place a player in the top 15% players taking part in the basketball championship? 9.10 points per game 10.57 points per game 10.95 points per game 12.35 points per game 13.96 points per game Question 13: A residual plot: displays residuals of the response variable versus the independent variable. displays residuals of the independent variable versus the response variable displays residuals of the independent variable versus residuals of the response variable. displays the independent variable versus the response variable. displays the response variable versus the dependent variable. Question 14: For any A and B random variables, which of the following statements must be true: I: μ_{A+B} = μ_{A} + μ_{B} II σ^{2}_{A-B} = σ^{2}_{A} + σ^{2}_{B} III σ^{2}_{A+B} = σ^{2}_{A} - σ^{2}_{B} I only. II only. I and II. II and II. I and II and II. Question 15: A random sample of 1000 balances in the retirement accounts of exempt employees of a company has a sample mean of μ_{1} = $100,000 and a standard deviation σ_{1} = $12,000. A random sample of 4000 balances in the retirement accounts of hourly employees of the same company has a sample mean of μ_{2} = $80,000 and a standard deviation σ_{2} = $14,000. If X is the sampling distribution of the differences in account balances of the two categories of employees, what is σ_{x}? $439.3 $2657.6 $5490.9 $11,065 $13,000 Question 16: Four children are asked to pick their favorite ice cream flavor out of 8 different flavors, and each of them is equally likely to pick any of the eight ice cream flavors. What is the probability that each child orders a different ice cream type? 5/72 2/5 7/64 105/256 45/128 Question 17: The rainfall of a county is measured for 14 years in a row to ascertain the local corn crop. No irrigation was used during this time. VariableCoefficients.e. of coefficient Constant33.8 Rainfall1.45.422 Find the 96% confidence interval for the slope of the least squares regression line. 1.45 +/- .056 1.45 +/- .972 1.45 +/- 1.1 33 +/- .972 33 +/- .645 Question 18: An electronics company designs and manufactures DC voltage power supplies. The output voltages of the power supplies have accuracy errors that are caused by three independent internal circuits: A, B and C. Past measurements have shown that circuit A creates an error with a mean of 100mV and a standard deviation of 20mV, circuit B creates an error with a mean of 80mV and a standard deviation of 10mV and circuit C creates an error with a mean of 50mV and a standard deviation of 10mV. What is the standard deviation of the error of the power supplies caused by all three circuits? 12mV 24.5mV 32.5mV 40mV 55mV Question 19: An opinion survey will be conducted at three corporations. Corporation A has 40,000 employees, corporation B has 60,000 employees and corporation C has 125,000 employees. The results of each survey will be used to estimate the opinions of employees at each corporation. Each survey will be conducted with a simple random sample of 500 employees. Which corporation will have its employees opinions estimated more accurately by the surveys? Corporation A. Corporation B. Neither corporation will have a more accurate estimate. Corporation C. Corporations A and B. Question 20: The quality department of an electronics manufacturer randomly selected 100 resistors. The mean resistance of the resistors was 201.5Ω and the standard deviation was .4Ω. Find the 98% confidence interval for this problem. 201.5+/-.093 201.5+/-.125 201.5+/-.133 201.5+/-.155 201.5+/-.212 Question 21: The heights of 100 students are normally distributed with a mean of 172cm. What is the standard deviation of the heights given that the probability of a height above 180cm is .25? 7.9cm 8.7cm 9.9cm 10.5cm 11.9cm Question 22: Six hundreds travelers have purchased airline tickets through the same travel agency. The following table gives the two-way classification of their destination choices. What is the joint relative conditional frequency for female travelers to Asia if the marginal row totals are fixed? MaleFemaleTotals Europe189195384 Asia4962111 South America5550105 Totals293307600 a) 53% b) 56% c) 58% d) 61% e) 63% Question 23: Out of the 500 students of a school, 30% wear glasses. If we use a simple random sample of 25 students, which of the following statements is correct: The sampling distribution is small relative to the population. The sampling distribution is a skewed distribution. The sampling distribution is normal. The mean of the sampling distribution is equal to .3. None of the above. Question 24: The mean of the weights of a group of 100 men and women is 160lb. If the number of men in the group is 60 and the mean weight of the men is 180lb, what is the mean weight of the women? a) 120lb b) 125lb c) 130lb d) 132lb e) 135lb Question 25: A real estate agent finds home buyers and closes the sales for 70% of his clients that sell thier houses. What is the mean number of sales for his next 10 clients and what is the standard deviation of this distribution? mean = 7 and standard deviation = 1.45 mean = 7 and standard deviation = 2.5 mean = 10 and standard deviation = 1.45 mean = 10 and standard deviation = 2.5 mean = 7 and standard deviation = 1.33 Question 26: The height and the weight of 18 students were measured and a scatterplot of the measures is shown below. If two pairs of measurements need to be removed from the set of 18, which of the choices shown below decreases the coefficient of correlation the most? a) S_{2} and S_{3} b) S_{2} and S_{5} c) S_{1} and S_{3} d) S_{2} and S_{4} e) S_{1} and S_{2} Question 27: It takes different times for different workers to perform the same specific task, as it is shown in the distribution below. The boxplot displays time in minutes. Which of the following statements must be true? a) The 25th percentile is greater than 70 minutes. b) The distribution is skewed to the left. c) The interquartile range is higher than 20 minutes. d) distribution median < distribution mean e) distribution median = distribution mean Question 28: Six fruit baskets contain peaches, apples and oranges. Three of the baskets contain two apples and one orange each, two other baskets contain three apples and one peach each, and the last basket contains two peaches and two oranges. You select a basket at random and then select a fruit at random from the basket. Which of the following is the probability that the fruit is an apple? .32 .4 .46 .5 .58 Question 29: A pharmaceutical company claims that its weight loss drug allows women to lose 8.5lb after one month of treatment. If we want to conduct an experiment to determine if the patients are losing less weight than advertised, which of the following hypotheses should be used? H0: μ = 8.5; Ha: μ > 8.5 H0: μ = 8.5; Ha: μ ≠ 8.5 H0: μ = 8.5; Ha: μ < 8.5 H0: μ ≠ 8.5; Ha: μ < 8.5 H0: μ ≠ 8.5; Ha: μ > 8.5 Question 30: A car manufacturer claims that 90% of their cars do not experience engine failures before reaching a mileage of 150,000 miles. A sample of 65 cars is investigated and 9 of the cars had an engine failure before 150,000 miles. Which of the following is an appropriate test outcome? z = 0.552 p = .214 z = -0.274 p = .214 z = -0.274 p = .151 z = -1.034 p = .214 z = -1.034 p = .151 Question 31: A tutoring company tests the results of their intensive training for a standardized test. Six students randomly selected have taken the test before and after having been trained by the company. The following table gives the test scores of the 6 students: Before8879778369 After7854837371 The appropriate test for this situation is: a matched pair t-test a chi-square goodness of fit test a two-sample z-test a one-sample t-test a one-sample z-test Question 32: The Department of Transportation of the State of New York claimed that it takes an average of 200 minutes to travel by train from New York to Buffalo. A random sample of 40 trains was taken and the average time required to travel from New York to Buffalo was 188 minutes, with a standard deviation of 28 minutes. What is the p-value for this test? .0355 .0099 .1294 .2881 .1167 Press the Submit button to see the results. Examples of AP Statistics Free Response Problems