AP Stats: Midterm Review
B
A biology teacher has just finished grading a quiz for a class of 26 students and has calculated measures of center and spread on the scores. While writing the grades on the quizzes, he realizes he made a mistake, and the highest grade should be 10 points higher. Which of the following sets of measurements will he have to recalculate? a) the mean and median b) the median and standard deviation c) the median and interquartile range d) the interquartile range and standard deviation e) the mean, standard deviation, and interquartile range
D
A forester studying oak trees finds that the correlation between x= the age (measured in years) and y= height (in feet) of a sample of trees is 0.78. Which of the following statements must be true? a) 78% of the variability in tree heights can be explained by variation on the trees' ages. b) for every year a tree ages, its height increases on average by 78%. c) if we let x= height of trees and y= age of trees, then the correlation would be the reciprocal of 0.78. d) if we measure the height in meters instead of feet, the correlation would still be 0.78. e) the unit for correlation in this context is foot-years.
D
A political action committee sends out a questionnaire to randomly selected mailing addresses, asking people to rate the importance of a variety of economic and social issues facing the country. At the end of the questionnaire is an (optional) invitation to donate money to the organization. Which of the following statements about this survey is true? a) the survey results are invalid because it's impossible to word questions about politics without creating bias. b) the survey results are invalid because only surveys conducted by phone are free from bias. c) the survey results will underestimate support for this political action committee in the entire population because people who respond are less likely to support an organization that asks for money. d) the survey results will overestimate support for this political action committee in the entire population because people more likely to respond if they are prepared to donate money. e) since the survey was sent to randomly selected households, it should be free of bias.
C
A recent investigation of prices for five-year-old Toyota Camrys in Montgomery, Alabama, and New York, New York, revealed that the mean price in Montgomery was $13,200 with a standard deviation of $1000. In New York, the mean price was $12,800 with a standard deviation of $1800. Which of the following statements is true? a) a car priced at $13,000 would have a negative standard score in both cities. b) the standard score of a car priced at $10,000 would be lower in New York than in Montgomery c) the standard score for a car priced at $15,000 would be higher in Montgomery than in New York. d) a car with a standardized score of 0 in Montgomery would have a negative standard score in New York e) a car with a standardized score of 0 in New York would also have a standardized score of 0 in Montgomery.
E
A track coach wants to test the effectiveness of a new training program for distance runners. He selects his fastest two runners and, using a coin flip, randomly chooses one to participate in the new program. The other will continue with the standard training program. He then picks the next two fastest runners and randomly assigns one to each program. He repeats this process with all his group of two runners. What is the name of the kind of experimental design? a) completely randomized design b) randomized block design c) stratified random design d) non-random pairs design e) matched pairs design
B
All of the following small data sets have a mean of 5. Which one has the lowest standard deviation? a) 1 1 5 5 5 9 9 b) 1 3 5 5 5 7 9 c) 1 1 5 9 9 d) 1 3 5 7 9 e) 1 1 9 9
B
An airline has 10 daily flights from Philadelphia to Denver. To assess customer satisfaction, a random sample of 15 passengers from each flight on a single day are asked to fill out a survey about their experience on the flight. What type of sample is this? a) simple random sample b) stratified random sample c) multistage sample d) cluster sample e) convenience sample
A
An efficiency consultant determines that on the assembly line at Widget Manufacturing, there is a strong, negative, linear relationship between x= the number of consecutive hours a worker has been assembling widgets and y= the number of widgets he can produce in an hour. He finds that 70% of the variation in widgets produced per hour can be explained by the regression of y on x. Which of the following is the best approximation of the correlation of x and y? a) -0.84 b) -0.7 c) -0.49 d) 0.49 e) 0.84
C
For the track coach's study described in the previous exercise, which of the following best describes a conclusion that can be drawn? a) we can determine whether race times improve for runners in the new program, but we can't establish cause and effect b) we can determine whether the new training program improves race times more than the standard program for any distance runner. c) we can determine whether the new training program improves race times more than the standard program for the distance runners in this study d) we cannot draw any conclusions, since all the volunteers are already members of the coach's team e) we cannot draw any conclusions, because there was no control group
A
Forty pound bags of bird seed do not have exactly 40 pounds of seed, but the weight of the seeds is approximately normally distributed with a mean of 40 pounds and a standard deviation of 0.25 pounds. Which of the following is the best estimate for the 90th percentile for the weight of these bags of seed? a) 40.3 pounds b) 40.4 pounds c) 40.5 pounds d) 41 pounds e) 43.2 pounds
D
If you flip three coins, the probability of getting three heads is 0.125. Which of the following statements follows this? a) if you flip three coins 1000 times, you will get three heads exactly 125 times b) if you get three heads in half of the first 100 set of flips, the probability that the next set of flips will produce three heads is slightly lower c) if you flip three coins 20 times, then at least one set of flips will be three heads d) if you flip three coins 5000 times, the percentage of time you get three heads will be very close to 12.5% e) if you get three heads four times in a row, the probability of getting three tails four times in a row increases.
D
One flight---Philadelphia to West Palm Beach, FL ---is 953 miles long and costs $110. Which of the following expressions correctly represents the residual for this data point? a) 101.24+0.02977 * 953 b) 953-(101.24+ 0.02977 * 110) c) (101.24 + 0.02977 * 110) - 953 d) 110- (101.24 + 0.02977 * 953) e) (101.24 + 0.02977 * 953) - 110
D
Some studies of the relationship between car color and frequency of accidents have found that red cars are more likely to be in accidents than black cars, despite how visible they are. Some experts warn that we should not conclude that red cars are less safe than black cars, because of possible cofounding. Which of the following best describes what this means. a) it can be hard to determine whether red cars or black cars are more visible on modern highways. b) much of the data on car color and accidents is contradictory, thus making it hard to draw definitive conclusions. c) much of the data on car color and accidents is subject to bias, thus making it hard to draw definitive conclusions. d) studies of this type are all observational, and it is not possible to separate the effect of car color from the type of people who choose to drive red cars. e) there are too many variables involved in traffic accidents to isolate the effect of car color.
E
The five-number summary of the weights (in grams) of 1200 tomatoes grown in a certain greenhouse was 90 113.5 140 161 236. How many tomatoes weighed less than 161 grams? a) 140 b) 236 c) 300 d) 600 e) 900
C
The least squares regression line minimizes which of the following quantities? a) the sum of the squared differences between the observed values of the response variable and the mean of the response variable b) the sum of the squared differences between the observed values of the explanatory variable and the mean of the explanatory variable c) the sum of the squared differences between the observed values of the response variable and the predicted values of the response variable d) the sum of the squared differences between the observed values of the explanatory variable and the predicted values of the explanatory variable e) the sum of the squared differences between the predicted values of the explanatory variable and the mean of the explanatory variable
A
The protein content for the 15 bean varieties has a mean of 12.2 grams and a standard deviation of 5.3 grams. The mean carbohydrate content is 33.6 grams with a standard deviation of 15.7 grams. The correlation is 0.84. Which of the following expressions represents the slope of the least squares regression of y= protein content on x= carbohydrate content? a) (0.84)(5.3)/(15.7) b) (0.84)(15.7)/(5.3) c) (0.84)(12.2)/(33.6) d) (0.84)(33.6)/(12.2) e) (33.6)/(0.84)(12.2)
D
The same 1200 tomatoes from question #9 have a mean weight of 143 grams and a standard deviation of 35 grams. If the weights are Normally distributed, approximately how many tomatoes weigh between 73 grams and 178 grams? a) 384 b) 600 c) 816 d) 978 e) 1140
D
The time it takes people to finish a certain kind of puzzle is strongly skewed right. Which of the following statements is true about the mean and median of this distribution? a) the mean and median will be exactly equal b) the mean and median will be approximately equal, but probably not exactly equal c) the mean will be less than the median d) the mean will be greater than the median e) which measure of center is greater depends on how strongly skewed the data is
A
The unusual point in the upper left part of the plot is for navy beans, with 15.8 grams of protein and 15.8 grams of carbohydrates. Which of the following best describes how correlation would change if we removed navy beans from the data set? a) the correlation would be closer to 1, because the remaining data would have a stronger positive relationship. b) the correlation would be closer to 1, because there would be fewer individuals in the data set. c) the correlation would be closer to 0, because the data would more closely resemble a straight line. d) the correlation would be closer to 0, because the standard deviation of the residuals would be smaller. e) correlation would no longer be calculated, because the remaining data would fall into two distinct groups.
B
What is the principle purpose of control in a randomized comparative experiment? a) eliminating bias b) isolating the effect of the treatment variable by keeping all other variables the same in the treatment groups c) creating treatment groups that are as similar as possible d) reducing the impact of random variation arising from random assignment to groups e) ensuring that an experiment is conducted in a double blind fashion
C
Which of the following best describes what S=20.7237 measures? a) the standard deviation of air fares b) the standard deviation of flight distances c) the standard deviation of the residuals d) the slope of the least squares regression line e) the standard deviation of the slope
C
Which of the following is NOT true about standard deviation? a) standard deviation is always non-negative b) standard deviation measures the typical distance between values in a data set and the mean value c) if the units for the data are in inches, standard deviation is in square inches d) standard deviation is very sensitive to outliers e) adding a value to the data set that is equal to the mean will decrease the standard deviation
B
Which of the following is the best description of a simple random sample of size n from a population of size N? a) any method of sampling in which individuals are selected in a completely haphazard fashion. b) any method of sampling in which every group of individuals of size n is equally likely to be selected. c) any method of sampling in which every individual is equally likely to be selected d) any method of sampling in which each individual has a probability of n/N of being selected. e) any method of sampling that involves the use of a random digits table
A
Which of the following is the most important reason for randomly assigning subjects to treatment groups in an experiment? a) to create groups that are as similar as possible b) to eliminate bias c) to create a double-blind design d) to reduce random variation e) to counteract the placebo effect
