AP Statistics Final

Items produced by a manufacturing process are supposed to weigh 90 grams. The manufacturing process is such, however that there is variability in the items produced and they do not all weigh exactly 90 grams. The distribution of weights can be approximated by a Normal distribution with mean 90 grams and a standard deviation of 1 gram. About what percentage of the items will either weigh less than 87 grams or more than 93 grams? a. 0.15% b. 0.3% c. 6% d. 94% e. 99.7%

0.3%

A company produces ceramic floor tiles that are supposed to have a surface area of 16.0 square inches. Due to variability in the manufacturing process, the actual surface area has a Normal distribution with a mean of 16.1 square inches and a standard deviation of 0.2 square inches. The proportion of tiles produced by the process with surface area less than 16.0 square inches is a. 0.1915 b. 0.3085 c. 0.3173 d. 0.4115 e. 0.6915

0.3085

The distribution of household incomes in a small town is strongly skewed to the right. The mean income is $42,000 and the standard deviation is $24,000. The Ames family's household income is $60,000. The z-score for the Ames family's income is a. -0.75 b. 0.3 c. 0.75 d. 0.86 e. None of these, because z-score cannot be used unless the distribution is Normal.

0.75

In a statistics course, a linear regression equation was computed to predict the final-exam score form the score on the first test. The equation was Y^ = 10+0.9x where y is the final-exam score and x is the score on the first test. Bill scored a 90 on the first test and a 93 on the final exam. What is the value of his residual? a. -2.0 b. 2.0 c. 3.0 d. 93 e. none of these

2.0

Suppose that 16-ounce bags of chocolate chip cookies are produced with weights that follow a Normal distribution with mean weight 16.1 ounces and standard deviation 0.1 ounce. The percent of bags that will contain between 16.0 and 16.1 ounces is about a. 20 b. 16 c. 34 d. 68 e. None of the above is correct.

34

A company produces packets of soap powder that are 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 0.7 oz. 95% of packets actually contain more than x oz. of soap powder. What is x? a. 31.60 b. 31.85 c. 32.88 d. 34.15 e. 34.40

34.15

Kitchen appliances don't last forever. The lifespan of all microwave ovens sold in the United States is approximately Normally distributed with a mean of 9 years and a standard deviation of 2.5 years. What percentage of the ovens last more than 10 years? a. 11.5% b. 34.5% c. 65.5% d. 69% e. 84.5%

34.5%

The 35th percentile of a population is the number x such that a. 35% of the population scores are above x. b. 65% of the population scores are above x. c. 35% of the population scores equal x. d. x is 35% of the population median. e. x is 35% of the population mean.

65% of the population scores are above x.

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 adult women in one of the countries. Country A: 92, 110, 120, 160, 240 About what percent of Country A women weigh between 110 and 240 pounds? a. 50% b. 65% c. 75% d. 85% e. 95%

75%

In a statistics course, a linear regression equation was computed to predict the final-exam score form the score on the first test. The equation was Y^ = 10+0.9x where y is the final-exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam? a. 85.5 b. 90 c. 95 d. 95.5 e. none of these

95.5

A set of data describes the relationship between the size of annual salary raises and the performance ratings for employees of a certain company. The least squares regression equation is y^= 1400+2000x where y is the raise amount (in dollars) and x is the performance rating. Which of the following statements is not necessarily true? a. For each one-point increase in performance rating, the raise will increase on average by $2000. b. The actual relationship between salary raises and performance rating is linear. c. A rating of 0 will yield a predicted raise of $1400. d. The correlation between salary raise and performance rating is positive. e. If the average performance rating is 1.2, then the average raise is $3800.

The actual relationship between salary raises and performance rating is linear.

All but one of the following statements contains an error. Which statement could be correct? a. There is a correlation of 0.54 between the position a football player plays and his weight. b. We found a correlation of r= -0.63 between gender and political party preference. c. The correlation between the distance travelled by a hiker and the time spent hiking is r= 0.9 meters per second. d. We found a high correlation between the height and age of children: r= 1.12. e. The correlation between mid-August soil moisture and the per-acre yield of tomatoes is r= 0.53.

The correlation between mid-August soil moisture and the per-acre yield of tomatoes is r= 0.53.

The mean birth weight of infants born at a certain hospital in the month of April was 128 oz. with a standard deviation of 10.2 oz. Which of the following is a correct interpretation of standard deviation? a. All the infants born in April weighed between 117.8 oz. and 138.2 oz. b. About half the infants born in April weighed between 117.8 oz. ad 138.2 oz. c. The difference between the mean weight and the median weight of infants born in April was 10.2 oz. d. The distance between the weight of each infant born in April and the mean weight was, on average, about 10.2 oz. e. The mean weight of infants born in subsequent months is likely to be within 10.2 oz. of the mean weight in April.

The distance between the weight of each infant born in April and the mean weight was, on average, about 10.2 oz.

A set of data has a mean that is much larger than the median. Which of the following statements is most consistent with this information? a. The distribution is symmetric. b. The distribution is skewed left. c. The distribution is skewed right. d. The distribution is bimodal. e. The data set probably has a few low outliers.

The distribution is skewed right.

If a distribution is skewed to the right, which of the following is true? a. The mean must be less than the median. b. The mean and median must be equal. c. The mean must be greater than the median. d.The mean is either equal to or less than the median. e. It's impossible to tell which of the above statements is true without seeing the data.

The mean must be greater than the median.

A sportswriter wants to know how strongly Lafayette residents support the local minor league baseball team, the Lafayette Leopards. She stands outside the stadium before a game and interviews the first 20 people who enter the stadium. The newspaper asks you to comment on their survey of local opinion. You say: a. This is a simple random sample. It gives very accurate results. b. This is a simple random sample. The results are not biased, but the sample is too small to have high precision. c. This is a census, because all fans had a chances to be asked. It gives very accurate results. d. This is a convenience sample. It will almost certainly overestimate the level of support among all Lafayette residents. e. This is a convenience sample. It will almost certainly underestimate the level of support among all Lafayette residents.

This is a convenience sample. It will almost certainly overestimate the level of support among all Lafayette residents.

To test the effect of music on productivity, a group of assembly line workers are given portable mp3 players to play whatever music they choose while working for one month. For another month, they work without music. The order of the two treatments for each worker is determined randomly. This is a. an observational study. b. a matched paris experiment. c. a completely randomized experiment. d. a block design, but not a matched pairs experiment. e. impossible to classify unless more details of the study are provided.

a matched paris experiment.

A data set is Normally distributed with a mean of 25 and a standard deviation of 8. If you calculate the standard score of every observation in this data set, the resulting scores will have a distribution that has a. a mean of 100 and a standard deviation of 10. b. a mean of 25 and a standard deviation of 10. c. a mean of 25 and a standard deviation of 1. d. a mean of 1 and a standard deviation of 1. e. a mean of 0 and a standard deviation of 1.

a mean of 0 and a standard deviation of 1.

A television station is interested in predicting whether voters in its viewing area are in favor of offshore drilling. It asks its viewers to phone in and indicate whether they support/are in favor of or are opposed to this practice. Of the 2241 viewers who phoned, 1574 (70%) were opposed to offshore drilling. The viewers who phoned in are a. a voluntary response sample. b. a convenience sample. c. a probability sample. d. a population. e. a simple random sample.

a voluntary response sample.

A researcher wishes to determine whether the rate of water flow (in liters per second) over an experimental soil bed can be used to predict the amount of soil washed away (in kilograms). In this study, the explanatory variable is a. amount of eroded soil. b. rate of water flow. c. size of soil bed. d. depth of soil bed. e. liters/second.

rate of water flow.

A sportswriter wants to know how strongly Lafayette residents support the local minor league baseball team, the Lafayette Leopards. She stands outside the stadium before a game and interviews the first 20 people who enter the stadium. The sample for the survey is a. all residents of Lafayette b. all Leopard fans. c. all people attending the game the day the survey was conducted. d. the 20 people who gave the sportswriter their opinion. e. the sportswriter.

the 20 people who gave the sportswriter their opinion.

A marketing research firm wishes to determine if the adult men in Laramie, Wyoming, would be interested in a new upscale men's clothing store. From a list of all residential addresses in Laramie, the firm selects a simple random sample of 100 and mails a brief questionnaire to each. The chance that all 100 homes in a particular neighborhood in Laramie end up being the sample of residential addresses selected is a. the same as for any other set of 100 residential addresses. b. exactly 0. Simple random samples will spread out the addresses selected. c. reasonably large due to the "cluster" effect. d. 100 divided by the size of the population of Laramie. e. large since the population of Laramie is small.

the same as for any other set of 100 residential addresses.

The proportion of scores in a standard Normal distribution that are greater than 1.25 is closest to: a. .1056 b. .1151 c. .1600 d. .8849 e. .8944

.1056

Using the standard Normal distribution tables, the area under the standard Normal curve corresponding to z> -1.22 is a. 0.1112. b. 0.1151. c. 0.4129. d. 0.8849. e. 0.8888.

0.8888

Suppose that 16-ounce bags of chocolate chip cookies are produced with weights that follow a Normal distribution with mean weight 16.1 ounces and standard deviation 0.1 ounce. Approximately what percent of the bags will likely be underweight (that is, less than 16 ounces)? a. 10 b. 16 c. 32 d. 64 e. None of the above

16

A nutritionist wants to study the effect of storage time (6, 12, and 18 months) on the amount of vitamin C present in freeze dried fruit when stored for these lengths of time. Vitamin C is measured in milligrams per 100 milligrams of fruit. Six fruit packs were randomly assigned to each of the three storage times. The treatment, experimental unit, and response are respectively: a. A specific storage time, amount of vitamin C, a fruit pack b. A fruit pack, amount of vitamin C, a specific storage time c. Random assignment, a fruit pack, amount of vitamin C d. A specific storage time, a fruit pack, amount of vitamin C e. A specific storage time, the nutritionist, amount of vitamin C

A specific storage time, a fruit pack, amount of vitamin C

The median age of five elephants at a certain zoo is 30 years. One of the elephants, whose age is 50 years, is transferred to a different zoo. The median age of the remaining four elephants is a. 40 years. b. 30 years. c. 25 years. d. less than 30 years. e. Cannot be determined from the information given.

Cannot be determined from the information given.

A professor records the values of several variables for each student in her class. These include the variables listed below. Which of these variables is categorical? a. Score on the final exam (out of 200 points). b. Final grade for the course (A, B, C, D, or F). c. The total number of points earned in the class (i.e., the total of the points on all exams and quizzes in the course; the maximum number of points possible is 500). d. The number of lectures the student missed. e. Amount of time, in minutes, spent studying for the final exam.

Final grade for the course (A, B, C, D, or F).

Simple random sampling a. reduces bias resulting from poorly worded questions. b. offsets bias resulting from undercoverage and nonresponse. c. reduces bias resulting from the behavior of the interviewer. d. reduces variability. e. None of the above.

None of the above.

A small company that prints custom t-shirts has 6 employees, one of whom is the owner and manager. Suppose the owner makes $120,000 per year and the other employees make between $40,000 and $50,000 per year. One day, the owner decides to give himself a $30,000 raise. Which of the following describes how the company's mean and median salaries would change? a. The mean and median would both increase by $5,000. b. The mean would increase by $5,000 and the median would not change. c. The mean would increase by $6,000 and the median would not change. d. The median would increase by $6,000 and the mean would not change. e. The mean would increase by $6,000, but we cannot determine the change in the median without more information.

The mean would increase by $5,000 and the median would not change.

A stratified random sample is appropriate when a. It is impractical to take a simple random sample because the population is too large. b. The population can be easily subdivided into groups according to some categorical variable, and the variable you are measuring is quite different within the groups but very similar between groups. c. The population can be easily subdivided into groups according to some categorical variable, and the variable you are measuring is very similar within the groups but quite different between groups. d. You intend to take a sample of more than 100 individuals. e. You want to avoid undercoverage of certain groups.

The population can be easily subdivided into groups according to some categorical variable, and the variable you are measuring is very similar within the groups but quite different between groups.

A survey is to be administered to recent graduates of a certain nursing school in order to compare the starting salaries of women and men. For a random sample of graduates, three variables are to be recorded: sex, starting salary, and area of specialization. Which of the following best describes a conclusion that can be drawn from this study? a. Whether being female causes graduates of this nursing school to have lower (or higher) starting salaries than males. b. Whether being female causes graduates in this sample to have lower (or higher) starting salaries than males. c. Whether choosing certain area of specialization causes females graduates of this nursing school to have lower (or higher) starting salaries than males. d. Whether there is an association between sex and starting salary among graduates of this nursing school. e. Whether there is an association between sex and starting salary at all nursing schools similar to this one.

Whether there is an association between sex and starting salary among graduates of this nursing school.

A sportswriter wants to know how strongly Lafayette residents support the local minor league baseball team, the Lafayette Leopards. She stands outside the stadium before a game and interviews the first 20 people who enter the stadium. The intended population for this survey is a. all residents of Lafayette. b. all Leopard fans. c. all people attending the game the day the survey was conducted. d. the 20 people who gave the sportswriter their opinion. e. all American adults.

all residents of Lafayette

A researcher observes that, on average, the number of divorces in cities with Major League Baseball teams is larger than in cities without Major League Baseball teams. Te most plausible explanation for this observed association is that the a. presence of a Major League Baseball team causes the number of divorces to rise (perhaps husbands are spending too much time at the ballpark). b. high number of divorces is responsible for the presence of Major League Baseball teams (more single men means potentially more fans at the ballpark, making it attractive for an owner to relocate to such cities). c. association is due to the presence of a lurking variable (Major League teams tend to be in large cities with more people, hence a greater number of divorces). d. association makes no sense, since many married couples go to the ballpark together. e. observed association is purely coincidental. It is implausible to believe the observed association could be anything other than accidental.

association is due to the presence of a lurking variable (Major League teams tend to be in large cities with more people, hence a greater number of divorces).

The five-number summary of the distribution of scores on the final exam in Psych 001 last semester was: 18 39 62 76 100 The 80th percentile was: a. 76 b. between 18 and 39 c. between 62 and 76 d. between 76 and 100 e. probably between 39 and 76, since most of the class scored between these two numbers.

between 76 and 100

A maple sugar manufacturer wants to estimate the average trunk diameter of Sugar Maples trees in a large forest. There are too many trees to list them all and take a SRS, so he divides the forest into several hundred 10 meter by 10 meter plots, selects 25 plots at random, and measures the diameter of every Sugar Maple in each one. This is an example of a a. multistage sample. b. stratified sample. c. simple random sample. d. cluster sample. e. convenience sample.

cluster sample.

To determine the proportion of each color of Peanut Butter M&Ms, you buy 10 1.69 ounce packages and count how many there are of each color. This is an example of a. simple random sampling b. cluster sampling c. multistage sampling d. stratified random sampling e. systematic random sampling

cluster sampling

Control groups are used in experiments in order to a. control the effects of outside variables on the outcome. b. control the subjects of a study to ensure that all participate equally. c. guarantee that someone other than the investigators, who have a vested interest in the outcome, controls how the experiment is conducted. d. achieve a proper and uniform level of randomization. e. reduce the variability in results.

control the effects of outside variables on the outcome.

Other things being equal, larger automobile engines consume more fuel. You are planning an experiment to study the effect of engine size (in liters) on the gas mileage (in miles per gallon) of sport utility vehicles. In this study, a. gas mileage is a response variable, and you expect to find a negative association. b. gas mileage is a response variable, and you expect to find a positive association. c. gas mileage is an explanatory variable, and you expect to find a strong negative association. d. gas mileage is an explanatory variable, and you expect to find a strong positive association. e. gas mileage is an explanatory variable, and you expect to find very little association.

gas mileage is a response variable, and you expect to find a negative association.

There are three children in a room, ages three, four, and five. If a four-year-old child enters the room the a. mean age will stay the same but the variance will increase. b. mean age will stay the same by the variance will decrease. c. mean age and variance will stay the same. d. mean age and variance will increase. e. mean age and variance will decrease.

mean age will stay the same but the variance will decrease.

A new headache remedy was given to a group of 25 subjects who had headaches. Four hours after taking the new remedy, 20 of the subjects reported that their headaches had disappeared. From this information you can conclude a. that the remedy is effective for the treatment of headaches. b. nothing, because the sample size is too small. c. nothing, because there is no control group for comparison. d. that the new treatment is better than aspirin. e. that the remedy is not effective for the treatment of headaches.

nothing, because there is no control group for comparison.

A researcher for a consumer products company is field testing a new formula for laundry detergent. He has contracted with 60 families, each with two children, who have agreed to test the product. He randomly assigns 30 families to the group that will use the new formula and 30 to the group that will use the company's current detergent formula. The most important reason for this random assignment is that a. randomization makes the analysis easier since the data can be collected and entered into the computer in any order. b. randomization eliminates the impact of any confounding variables. c. randomization is a good way to create two groups of 30 families that are as similar as possible, so that comparisons can be made between the two groups. d. randomization ensures that the study is double-blind. e. randomization reduces the impact of outliers.

randomization is a good way to create two groups of 30 families that are as similar as possible, so that comparisons can be made between the two groups.

The principle reason for replication in designing experiments is that it a. distinguishes a treatment effect from the effects of confounding variables. b. allows double-blinding. c. reduces sampling variability. d. creates approximately equal groups for comparison. e. eliminates the placebo effect.

reduces sampling variability.

A study of elementary school children, ages 6 to 11, find s a high positive correlation between shoe size x and score y on a test of reading comprehension. The observed correlation is most likely due to a. the effect of a lurking variable, such as age. b. a mistake, since the correlation must be negative. c. cause and effect (larger shoe size causes higher reading comprehension). d. "reverse' cause and effect (higher reading comprehension causes larger shoe size). e. several outliers in the data set

the effect of a lurking variable, such as age.

The correlation between the heights of fathers and the heights of their (fully grown) sons is r= 0.52. This value was based on both variables being measured in inches. If fathers' heights were measured in feet (one foot equals 12 inches), and sons' heights were measured in furlongs (one furlong equals 7920 inches), the correlation between heights of fathers and heights of sons would be a. much smaller than 0.52 b. slightly smaller than 0.52 c. unchanged: equal to 0.52 d. slightly larger than 0.52 e. much larger than 0.52

unchanged: equal to 0.52

Just before the presidential election of 1936, the magazine Literary Digest predicted--incorrectly, as it turned out-- that Alf Landon would defeat Franklin Delano Roosevelt. Landon lost in a landslide. It turned out that the magazine had only polled its own subscribers, plus others from a list of automobile owners and a list of people who had telephone service. All three groups had higher than typical incomes during the Great Depression. This is an example of a. voluntary response bias. b. bias resulting from question wording. c. undercoverage. d. nonresponse. e. response bias.

undercoverage

Which of the following statements are true? I. The area under a Normal curve is always 1, regardless of the mean and standard deviation. II. The mean is always equal to the median for any Normal distribution. III. The interquartile range for any Normal curve extends from u-o to u+o a. I and II b. I and III c. II and III d. I, II, and III e. None of the above gives the correct set of true statements.

I and II

The mean speed of vehicles in the "cars only" lanes of the New Jersey turnpike is 68 miles per hour. The mean speed of vehicles in the "any vehicle" lanes is 64 miles per hour. What must be true about the mean speed of all vehicles on the turnpike, assuming these are the only types of lanes? a. It could be any number between 64 and 68 miles per hour. b. It must be larger than the median speed. c. It must be larger than 66 miles per hour. d. It must be 66 miles per hour. e. We don't have enough information to draw any conclusion about the mean speed of all vehicles.

It could be any number between 64 and 68 miles per hour.

Jack and Jill are both enthusiastic players of a certain computer game. Over the past year, Jack's mean score when playing a game is 12,400 with a standard deviation of 1500. During the same period, Jill's mean score is 14,200, with a standard deviation of 2000. They devise a fair contest: each one will play the game once, and they will compare z-scores. Jack gets a score of 14,000, and Jill gets a score of 16,000. Who won the contest, and what were each of their z-scores? a. Jack's z= 1.07; Jill's z= 1.11, Jill wins the contest b. Jack's z= 1.07; Jill's z= 0.90; Jack wins the contest c. Jack's z= 0.94; Jill's z= 1.11; Jill wins the contest d. Jack's z= 0.94; Jill's z= 0.90; Jack wins the contest e. Jack's z= 0.81; Jill's z= 0.99; Jill wins the contest

Jack's z= 1.07; Jill's z= 0.90; Jack wins the contest

A survey was done in the town of Mechanicsville to estimate the proportion of cars that are red and made by companies based in Japan. A random sample of 25 cars from a student parking lot at Lee-Davis High School was taken. Which of the following statements is not correct? a. This sample may not be representative of the cars in Mechanicsville because mainly students park at Lee-Davis High School. b. If the particular parking space is vacant, we can simply select another parking space at random because it is unlikely that a space being vacant is related to the color of manufacturer of the car. c. It would be an error to simply select the first 25 parking spaces in the lot closest to the auditorium because there are a number of parking spaces there reserved for Drivers Ed vehicles, whose primary color is white. d. A different team doing the sampling independently would obtain different answers for their sample proportions. e. The results will be the same regardless of the time of day that the sample is taken.

The results will be the same regardless of the time of day that the sample is taken.

A statistics teacher asks the 29 students in his statistics class how many minutes they spent on one homework assignment. The distribution of the variable "time on homework" is a. the difference between the longest time and the shortest time among the students' responses. b. a description of what value the variable takes and how often it takes them. c. the average distance between each value of the variable. d. the average time the students spent on the assignment. e. the number of students who were asked the questions-- that is, 29.

a description of what values the variable takes and how often it takes them.