ALL AP Practice Tests Chap 1-8
Which of the following is not correct about a standard Normal distribution?
The proportion of scores that satisfy z > −3.0 is 0.9938
China has 1.2 billion people. Marketers want to know which international brands they have heard of. A large study showed that 62% of all Chinese adults have heard of Coca-Cola. You want to simulate choosing a Chinese at random and asking if he or she has heard of Coca-Cola. One correct way to assign random digits to simulate the answer is:
Two digits simulate one person's answer; 00 to 61 mean "Yes" and 62 to 99 mean "No."
Which of the following bar graphs is equivalent to the pie chart in Question T1.2? [ pie chart of us, france, japan, sweden, italy, and germany ]
Us is MUCH bigger than all other bars, incredibly right skewed
A study of treatments for angina (pain due to low blood supply to the heart) compared bypass surgery, angioplasty, and use of drugs. The study looked at the medical records of thousands of angina patients whose doctors had chosen one of these treatments. It found that the average survival time of patients given drugs was the highest. What do you conclude?
We can't conclude that drugs prolong life because this was an observational study.
Suppose a student is randomly selected from your school. Which of the following pairs of random variables are most likely independent?
X = average amount of homework the student does per night; Y = student's height
A school guidance counselor examines the number of extracurricular activities that students do and their grade point average. The guidance counselor says, "The evidence indicates that the correlation between the number of extracurricular activities a student participates in and his or her grade point average is close to zero." A correct interpretation of this statement would be that
there is no linear relationship between number of activities and grade point average for students at this school
When we take a census, we attempt to collect data from
every individual in the population
The fraction of the variation in the values of y that is explained by the least-squares regression of y on x is
the square of the correlation coefficient.
A deck of playing cards has 52 cards, of which 12 are face cards. If you shuffle the deck well and turn over the top 3 cards, one after the other, what's the probability that all 3 are face cards?
0.010
Seventeen people have been exposed to a particular disease. Each one independently has a 40% chance of contracting the disease. A hospital has the capacity to handle 10 cases of the disease. What is the probability that the hospital's capacity will be exceeded?
0.035
What is the probability that a student has a GPA under 2.0? [ gpa by skipped classes two way table ]
0.255
Until the scale was changed in 1995, SAT scores were based on a scale set many years ago. For Math scores, the mean under the old scale in the 1990s was 470 and the standard deviation was 110. In 2009, the mean was 515 and the standard deviation was 116. What is the standardized score (z-score) for a student who scored 500 on the old SAT scale?
0.27
What is the probability that a student has a GPA under 2.0 or has skipped many classes? [ gpa by skipped classes two way table ]
0.285
Value: 1 || 2 || 3 || 4 Probability : 0.2 || 0.4 || 0.3 || 0.1 What is the probability that a randomly chosen subject completes more than the expected number of puzzles in the five-minute period while listening to soothing music?
0.4
Choose an American adult at random. The probability that you choose a woman is 0.52. The probability that the person you choose has never married is 0.25. The probability that you choose a woman who has never married is 0.11. The probability that the person you choose is either a woman or has never been married (or both) is therefore about
0.66
What is the probability that a student has a GPA under 2.0 given that he or she has skipped many classes? [ gpa by skipped classes two way table ]
0.727
Suppose we select an SRS of size n = 100 from a large population having proportion p hat of successes. Let p hat be the proportion of successes in the sample. For which value of p would it be safe to use the Normal approximation to the sampling distribution of p hat?
0.85
Value: 1 || 2 || 3 || 4 Probability : 0.2 || 0.4 || 0.3 || 0.1 Let D be the difference in the number of puzzles solved by two randomly selected subjects in a five-minute period. What is the standard deviation of D?
1.27
You want to compute a 90% confidence interval for the mean of a population with unknown population standard deviation. The sample size is 30. The value of t* you would use for this interval is
1.699
A researcher initially plans to take an SRS of size n from a population that has mean 80 and standard deviation 20. If he were to double his sample size (to 2n), the standard deviation of the sampling distribution of the sample mean would be multiplied by
1/sqrt of 2
Many television viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, Timex Group USA wishes to estimate the proportion of consumers who believe what is shown in Timex television commercials. Let p represent the true proportion of consumers who believe what is shown in Timex television commercials. What is the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05 or less at a 99% confidence level?
700
A study of voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election. Election records show that only 56% of registered voters voted in the election. Which of the following statements is true about the boldface numbers?
72% is a statistic and 56% is a parameter.
Scientists examined the activity level of 7 fish at different temperatures. Fish activity was rated on a scale of 0 (no activity) to 100 (maximal activity). The temperature was measured in degrees Celsius. A computer regression printout and a residual plot are given below. Notice that the horizontal axis on the residual plot is labeled "Fitted value." [ fitted value by residual residual plot ] What was the activity level rating for the fish at a temperature of 20°C?
87
Computer voice recognition software is getting better. Some companies claim that their software correctly recognizes 98% of all words spoken by a trained user. To simulate recognizing a single word when the probability of being correct is 0.98, let two digits simulate one word; 00 to 97 mean "correct." The program recognizes words (or not) independently. To simulate the program's performance on 10 words, use these random digits: 60970 70024 17868 29843 61790 90656 87964 The number of words recognized correctly out of the 10 is
9
A 90% confidence interval for the mean μ of a population is computed from a random sample and is found to be 9 ± 3. Which of the following could be the 95% confidence interval based on the same data?
9 ± 4
The Gallup Poll interviews 1600 people. Of these, 18% say that they jog regularly. The news report adds: "The poll had a margin of error of plus or minus three percentage points at a 95% confidence level." You can safely conclude that
95% of all Gallup Poll samples like this one give answers within ± 3% of the true population value.
In preparing to construct a one-sample t interval for a population mean, suppose we are not sure if the population distribution is Normal. In which of the following circumstances would we not be safe constructing the interval based on an SRS of size 24 from the population?
A boxplot of the data has a large outlier
The weight of tomatoes chosen at random from a bin at the farmer's market follows a Normal distribution with mean μ = 10 ounces and standard deviation σ = 1 ounce. Suppose we pick four tomatoes at random from the bin and find their total weight T. The random variable T is
Normal, with mean 40 ounces and standard deviation 2 ounces
Many professional schools require applicants to take a standardized test. Suppose that 1000 students take such a test. Several weeks after the test, Pete receives his score report: he got a 63, which placed him at the 73rd percentile. This means that
Pete did better than about 73% of the test takers
Consider an experiment to investigate the effectiveness of different insecticides in controlling pests and their impact on the productivity of tomato plants. What is the best reason for randomly assigning treatment levels (spraying or not spraying) to the experimental units (farms)?
Random assignment will tend to average out all other uncontrolled factors such as soil fertility so that they are not confounded with the treatment effects.
A test for extrasensory perception (ESP) involves asking a person to tell which of 5 shapes—a circle, star, triangle, diamond, or heart—appears on a hidden computer screen. On each trial, the computer is equally likely to select any of the 5 shapes. Suppose researchers are testing a person who does not have ESP and so is just guessing on each trial. What is the probability that the person guesses the first 4 shapes incorrectly but gets the fifth correct?
(4/5)^4*(1/5)
A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the amount poured into the bottles follows a Normal distribution with mean 16.05 ounces and standard deviation 0.1 ounce. Assume that the machine is working properly. If four bottles are randomly selected and the number of ounces in each bottle is measured, then there is about a 95% chance that the sample mean will fall in which of the following intervals?
15.95 to 16.15 ounces
The weights (in pounds) of three adult males are 160, 215, and 195. The standard error of the mean of these three weights is
16.07
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 hat = 25.2 + 3.3x, where x is the number of chirps per minute and y hat is the estimated temperature in degrees Fahrenheit. What is the predicted increase in temperature for an increase of 5 chirps per minute?
16.5°F
You record the age, marital status, and earned income of a sample of 1463 women. The number and type of variables you have recorded is
2 quantitative, 1 categorical
Choose an American household at random and record the number of vehicles they own. Here is the probability model if we ignore the few households that own more than 5 cars: number of cars - 0 || 1 || 2 || 3 || 4 || 5 probability - 0.09 || 0.36 || 0.35 || 0.13 || 0.05 || 0.02 A housing company builds houses with two-car garages. What percent of households have more cars than the garage can hold?
20%
For the Normal distribution shown, the standard deviation is closest to [ a normal unimodal distribution ]
3
If the heights of a population of men follow a Normal distribution, and 99.7% have heights between 5′0″ and 7′0″, what is your estimate of the standard deviation of the heights in this population?
4
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?
4.83 inches
The figure shows a cumulative relative frequency graph of the number of ounces of alcohol consumed per week in a sample of 150 adults who report drinking alcohol occasionally. About what percent of these adults consume between 4 and 8 ounces per week? [ percent by consumption(oz) line graph ]
40%
You want to take a simple random sample (SRS) of 50 of the 816 students who live in a dormitory on campus. You label the students 001 to 816 in alphabetical order. In the table of random digits, you read the entries 95592 94007 69769 33547 72450 16632 81194 14873 The first three students in your sample have labels
400, 769, 335
Forty students took a statistics examination having a maximum of 50 points. The score distribution is given in the following stem-and-leaf plot: 0 || 2 8 1 || 2 2 4 5 2 || 0 1 3 3 3 3 5 8 8 8 9 3 || 0 0 1 3 5 6 6 7 9 4 || 2 2 4 4 4 4 6 6 7 8 8 5 || 0 0 0 The third quartile of the score distribution is equal to
44
The percentage of students with less than $10 in their possession is closest to [ frequency by amount of money histogram ]
45%
Rainwater was collected in water collectors at 30 different sites near an industrial complex, and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are 4.60 and 1.10, respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error. The error can be corrected by adding 0.1 pH units to all of the values and then multiplying the result by 1.2. The mean and standard deviation of the corrected pH measurements are
5.64, 1.32
Earthquake intensities are measured using a device called a seismograph, which is designed to be most sensitive to earthquakes with intensities between 4.0 and 9.0 on the Richter scale. Measurements of nine earthquakes gave the following readings: [ 4.5 L 5.5 H 8.7 8.9 6.0 H 5.2 ] where L indicates that the earthquake had an intensity below 4.0 and an H indicates that the earthquake had an intensity above 9.0. The median earthquake intensity of the sample is
6.00
Suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their first year at a major university. The interval is to have a margin of error of $2. Based on last year's book sales, we estimate that the standard deviation of the amount spent will be close to $30. The number of observations required is closest to
609
What percent of all small companies receiving questionnaires responded? [ business size - two way table ]
62.5%
A TV station wishes to obtain information on the TV viewing habits in its market area. The market area contains one city of population 170,000, another city of 70,000, and four towns of about 5000 inhabitants each. The station suspects that the viewing habits may be different in larger and smaller cities and in the rural areas. Which of the following sampling designs would give the type of information that the station requires?
A stratified sample from the cities and towns in the market area
The figure shows the probability distribution of a discrete random variable X. Note that the cursor is on the histogram bar representing a value of 6. Which of the following best describes this random variable? [ normal float auto real radian cl ]
Binomial with n = 8, p = 0.3
Until the scale was changed in 1995, SAT scores were based on a scale set many years ago. For Math scores, the mean under the old scale in the 1990s was 470 and the standard deviation was 110. In 2009, the mean was 515 and the standard deviation was 116. Gina took the SAT in 1994 and scored 500. Her cousin Colleen took the SAT in 2013 and scored 530. Who did better on the exam, and how can you tell?
Gina-her standardized score is higher than Colleen's.
An experiment was conducted to investigate the effect of a new weed killer to prevent weed growth in onion crops. Two chemicals were used: the standard weed killer (C) and the new chemical (W). Both chemicals were tested at high and low concentrations on a total of 50 test plots. The percent of weeds that grew in each plot was recorded. Here are some boxplots of the results. Which of the following is NOT a correct statement about the results of this experiment?
High and low concentrations of either chemical have approximately the same effects on weed growth.
A radio talk show host with a large audience is interested in the proportion p of adults in his listening area who think the drinking age should be lowered to eighteen. To find this out, he poses the following question to his listeners: "Do you think that the drinking age should be reduced to eighteen in light of the fact that eighteen-year-olds are eligible for military service?" He asks listeners to phone in and vote "Yes" if they agree the drinking age should be lowered and "No" if not. Of the 100 people who phoned in, 70 answered "Yes." Which of the following conditions for inference about a proportion using a confidence interval are violated? I. The data are a random sample from the population of interest. II. The population is at least 10 times as large as the sample. III. n is so large that both n(p hat) and n(1 − p hat) are at least 10.
I only
An AP® Statistics student designs an experiment to see whether today's high school students are becoming too calculator-dependent. She prepares two quizzes, both of which contain 40 questions that are best done using paper-and-pencil methods. A random sample of 30 students participates in the experiment. Each student takes both quizzes—one with a calculator and one without— in a random order. To analyze the data, the student constructs a scatterplot that displays the number of correct answers with and without a calculator for each of the 30 students. A least-squares regression yields the equation. calculator hat = -1.2 + 0.865(pencil) r = 0.79 Which of the following statements is/are true? I. If the student had used Calculator as the explanatory variable, the correlation would remain the same. II. If the student had used Calculator as the explanatory variable, the slope of the least-squares line would remain the same. III. The standard deviation of the number of correct answers on the paper-and-pencil quizzes was larger than the standard deviation on the calculator quizzes.
I only
For events A and B related to the same chance process, which of the following statements is true?
If A and B are independent, then they cannot be mutually exclusive
The mean salary of all female workers is $35,000. The mean salary of all male workers is $41,000. What must be true about the mean salary of all workers?
It could be any number between $35,000 and $41,000.
Dr. Stats plans to toss a fair coin 10,000 times in the hope that it will lead him to a deeper understanding of the laws of probability. Which of the following statements is true?
It is likely that Dr. Stats will get about 50% heads.
A telephone poll of an SRS of 1234 adults found that 62% are generally satisfied with their lives. The announced margin of error for the poll was 3%. Does the margin of error account for the fact that some adults do not have telephones?
No. The margin of error only includes sampling variability.
A data set included the number of people per television set and the number of people per physician for 40 countries. The Fathom screen shot below displays a scatterplot of the data with the least-squares regression line added. In Ethiopia, there were 503 people per TV and 36,660 people per doctor. What effect would removing this point have on the regression line? [ pplpertv by pplperdoc scatterplot ]
Slope would decrease, y intercept would increase
Which of the following conclusions seems to be supported by the data? [ business size two way table ]
Small companies appear to have a higher response rate than medium or big companies.
Which of the following statements about this distribution is not correct? [ frequency by amount of money histogram ]
The IQR is $35
The figure shown is the density curve of a distribution. Seven values are marked on the density curve. Which of the following statements is true? [ a skewed left normal unimodal distribution ]
The area between A and G is 1
The number of undergraduates at Johns Hopkins University is approximately 2000, while the number at Ohio State University is approximately 60,000. At both schools, a simple random sample of about 3% of the undergraduates is taken. Each sample is used to estimate the proportion p of all students at that university who own an iPod. Suppose that, in fact, p = 0.80 at both schools. Which of the following is the best conclusion?
The estimate from Johns Hopkins has more sampling variability than that from Ohio State.
Which of the following random variables is geometric?
The number of digits I read in a randomly selected row of the random digits table until I find a 7
Value: 1 || 2 || 3 || 4 Probability : 0.2 || 0.4 || 0.3 || 0.1 The standard deviation of X is 0.9. Which of the following is the best interpretation of this value?
The number of puzzles solved by subjects typically differed from the mean by about 0.9 puzzles
The British government conducts regular surveys of household spending. The average weekly household spending (in pounds) on tobacco products and alcoholic beverages for each of 11 regions in Great Britain was recorded. A scatterplot of spending on alcohol versus spending on tobacco is shown below. Which of the following statements is true? [ alcohol by tobacco scatterplot plot ]
The observation in the lower-right corner of the plot is influential for the least-squares line.
You want to know the opinions of American high school teachers on the issue of establishing a national proficiency test as a prerequisite for graduation from high school. You obtain a list of all high school teachers belonging to the National Education Association (the country's largest teachers' union) and mail a survey to a random sample of 2500 teachers. In all, 1347 of the teachers return the survey. Of those who responded, 32% say that they favor some kind of national proficiency test. Which of the following statements about this situation is true?
The results of this survey may be affected by nonresponse bias
Which of the following statements about the sampling distribution of the sample mean is incorrect?
The sampling distribution shows how the sample was distributed around the sample mean.
Which of the following gives a correct interpretation of s in this setting?
The typical distance of the activity level ratings from the least-squares line is about 4.785 units.
You wonder if TV ads are more effective when they are longer or repeated more often or both. So you design an experiment. You prepare 30-second and 60-second ads for a camera. Your subjects all watch the same TV program, but you assign them at random to four groups. One group sees the 30-second ad once during the program; another sees it three times; the third group sees the 60-second ad once; and the last group sees the 60-second ad three times. You ask all subjects how likely they are to buy the camera.
This is a completely randomized design with two explanatory variables (factors).
Bias in a sampling method is
any difference between the sample result and the truth about the population that tends to occur in the same direction whenever you use this sampling method.
The student newspaper at a large university asks an SRS of 250 undergraduates, "Do you favor eliminating the carnival from the term-end celebration?" All in all, 150 of the 250 are in favor. Suppose that (unknown to you) 55% of all undergraduates favor eliminating the carnival. If you took a very large number of SRSs of size n = 250 from this population, the sampling distribution of the sample proportion p hat would be
approximately Normal with mean 0.55 and standard deviation 0.03.
The most important advantage of experiments over observational studies is that
experiments can give better evidence of causation.
The central limit theorem is important in statistics because it allows us to use the Normal distribution to find probabilities involving the sample mean
if the sample size is reasonably large (for any population).
Tonya wanted to estimate the average amount of time that students at her school spend on Facebook each day. She gets an alphabetical roster of students in the school from the registrar's office and numbers the students from 1 to 1137. Then Tonya uses a random number generator to pick 30 distinct labels from 1 to 1137. She surveys those 30 students about their Facebook use. Tonya's sample is a simple random sample because
it gave every possible sample of the same size an equal chance to be selected.
Consumers Union measured the gas mileage in miles per gallon of 38 vehicles from the same model year on a special test track. The pie chart provides information about the country of manufacture of the model cars tested by Consumers Union. Based on the pie chart, we conclude that [ pie chart of us, france, japan, sweden, italy, and germany ]
more than half of the cars in the study were from the United States.
Which of the following statements is not true of the correlation r between the lengths in inches and weights in pounds of a sample of brook trout?
r is measured in inches
The Gallup Poll has decided to increase the size of its random sample of voters from about 1500 people to about 4000 people right before an election. The poll is designed to estimate the proportion of voters who favor a new law banning smoking in public buildings. The effect of this increase is to
reduce the variability of the estimate
A researcher wishes to compare the effects of two fertilizers on the yield of soybeans. She has 20 plots of land available for the experiment, and she decides to use a matched pairs design with 10 pairs of plots. To carry out the random assignment for this design, the researcher should
subjectively divide the 20 plots into 10 pairs (making the plots within a pair as similar as possible) and then, for each pair, flip a coin to assign the fertilizers to the 2 plots
Suppose that you are a student aide in the library and agree to be paid according to the "random pay" system. Each week, the librarian flips a coin. If the coin comes up heads, your pay for the week is $80. If it comes up tails, your pay for the week is $40. You work for the library for 100 weeks. Suppose we choose an SRS of 2 weeks and calculate your average earnings x bar. The shape of the sampling distribution of x bar will be
symmetric but not Normal.
A Census Bureau report on the income of Americans says that with 90% confidence the median income of all U.S. households in a recent year was $57,005 with a margin of error of ±$742. This means that
the Census Bureau got the result $57,005 ± $742 using a method that will capture the true median income 90% of the time when used repeatedly.
When we standardize the values of a variable, the distribution of standardized values has mean 0 and standard deviation 1. Suppose we measure two variables X and Y on each of several subjects. We standardize both variables and then compute the least-squares regression line. Suppose the slope of the least-squares regression line is −0.44. We may conclude that
the correlation will also be − 0.44.
A certain vending machine offers 20-ounce bottles of soda for $1.50. The number of bottles X bought from the machine on any day is a random variable with mean 50 and standard deviation 15. Let the random variable Y equal the total revenue from this machine on a given day. Assume that the machine works properly and that no sodas are stolen from the machine. What are the mean and standard deviation of Y?
μY = $75, σY = $22.50
