Nine Weeks Exam

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 random order. To analyze the data, the student constructs a scatterplot that displays a linear association between the number of correct answers with and without a calculator for the 30 students. A least-squares regression yields the equation calculator = −1.2 + 0.865 (pencil) r=.79. Which of the following statements is/are true?

d. I and III only

The weights (in pounds) of three adult males are 160, 215, and 195. What is the standard error of the mean for these data?

d. 16.07

You record the age, marital status, and earned income of a sample of 1463 women. The number and type of variables you have recorded are:

d. 2 quantitative, 1 categorical

For the Normal distribution shown, the standard deviation is closest to

d. 3

Can texting make you healthier? Researchers randomly assigned 700 Australian adults to either receive usual health care or usual health care plus automated text messages with positive messages, such as "Walking is cheap. It can be done almost anywhere. All you need is comfortable shoes and clothing." The group that received the text messages showed a statistically significant increase in physical activity. What is the meaning of "statistically significant" in this context?

e. the difference in physical activity for the two groups is larger than the difference that could be expected to happen by chance alone

In class, there are 18 girls and 14 boys. If the teacher selects two students at random to attend a party with the principal, what is the probability that the two students are the same sex?

a. 0.49

The average yearly snowfall in Chillyville is approximately 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?

a. 4.83 inches

The central limit theorem is important in statistics because it allows us to use a Normal distribution to find probabilities involving the sample mean if the

a. Sample size is reasonably large (for any population)

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

a. 95% of all Gallop Poll samples like this one give answers within +/- 3% of the true proportion value

What is the probability that the person owns a Dodge or has four-wheel drive?

d. 90/125

The distribution of the time it takes for different people to solve a certain crossword puzzle is strongly skewed to the right with a mean of 30 minutes and a standard deviation of 15 minutes. The distribution of z-scores for those times is

d. skewed to the right with mean: 0 and standard deviation: 1

The students in Mr. Tyson's high school statistics class were recently asked if they would prefer a pasta party, a pizza party, or a donut party. The following bar graph displays the data. The graph is misleading because...

d. the vertical axis scale should start at zero

. What is the correlation between temperature and fish activity?

e. -0.95

95592 94007 69769 33547 72450 ...

e. 400, 760, 355

The dot plot displays the number of made shots in 100 simulated sets of 50 free throws by someone with probability 0.56 of making a free throw. Which of the following is an appropriate statement about Wilt's free-throw shooting based on this dot plot?

a. If wilt were still only a 56% shooter, the probability that he would make at least 34 of his shots is about 0.03

What was the actual activity level rating for the fish at a temperature of 20°C?

b. 84

A spinner has three equally sized regions: blue, red, and green. Jonny spins the spinner 3 times and gets 3 blues in a row. If he spins the spinner 297 more times, how many more blues is he most likely to get?

b. 99

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 18-year-olds are eligible for military service?" He asks listeners to go to his website and vote "Yes" if they agree the drinking age should be lowered and "No" if not. Of the 100 people who voted, 70 answered "Yes." Which of the following conditions are violated?

a. I only

A TV station wishes to obtain information on 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 residents 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 yield the type of information the station requires?

a. a stratified sample from the cities and towns in the market area

Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. Net weights vary slightly from bag to bag and are Normally distributed with mean mu. A representative of a consumer advocacy group wishes to see if there is convincing evidence that the mean net weight is less than advertised and so intends to test the hypotheses Null: mu: 1 Alternative: mu < 14 A Type I error in this situation would mean concluding that the bags

a. are being underfilled when they aren't

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?

b. 0.035

An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternative hypotheses you would use to test this claim are

b. Null: p= 0.5, Alternative: p> 0.5

The figure shows the probability distribution of a discrete random variable X. Which of the following best describes this random variable?

b. binomial with n=8, p= 0.3

A school guidance counselor examines how many extracurricular activities students participate in 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 0." Which of the following is the most appropriate conclusion?

e. No conclusion should be made based on the correlation without looking at a scatterplot of the data.

Which of the following has the greatest probability?

e. P(z< 2) if z is a standard Normal random variable

What is the probability that a randomly chosen subject completes more than the expected number of puzzles in the 5-minute period while listening to soothing music?

b. 0.4

Suppose we select an SRS of size n= 100 from a large population having a proportion p of successes. Let p-hat be the proportion of successes in the sample. For which value of p would it be safe to use a Normal approximation to the sampling distribution of p-hat?

c. 0.85

To determine the reliability of experts who interpret lie detector tests in criminal investigations, a random sample of 280 such cases was studied. The results were If the hypotheses are Null: Suspect is innocent versus Alternative: Suspect is guilty, which of the following is the best estimate of the probability that an expert commits a Type II error?

c. 15/140

If the heights of a population of men are approximately Normally distributed, and the middle 99.7% have heights between 5′0″ and 7′0″, what is the standard deviation of the heights in this population?

c. 4''

Which of the following gives a correct interpretation of s in this setting?

c. The typical distance of the activity level ratings from the least-squares line is about 4.785 units.

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

b. approximately Normal with mean 0.55 and a standard deviation of 0.03

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. Which of the following is the most appropriate conclusion?

d. 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

The standard deviation of X is 0.9. Which of the following is the best interpretation of this value?

d. the number of puzzles solves varies on average by about from the mean

Which of the following could be the median age?

b. 24 years

What is the probability that the person owns a Chevy, given that the truck has four-wheel drive?

b. 32/80

A newborn baby has extremely low birth weight (ELBW) if it weighs less than 1000 grams. A study of the health of such children in later years examined a random sample of 219 children. Their mean weight at birth was x-bar = 810 grams. This sample mean is an unbiased estimator of the mean weight μ in the population of all ELBW babies, which means that

b. in all possible samples of size 219 from this population, the mean of the values x-bar will equal mu

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

b. normal with mean 40 and standard deviation 2 ounces

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?

b. r is measured in inches

Which of the following conclusions seems to be supported by the data?

b. small companies have a larger response rate than medium or large companies

A random sample of 100 likely voters in a small city produced 59 voters in favor of Candidate A. The observed value of the standardized test statistic for performing a test of Null: p= 0.5 versus Alternative: p> 0.5 is which of the following?

b. z= (.59-.50)/ √(.5)(.5)/ 100

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 one correct?

c. P(X=5)= (4/ 5)^4 (1/ 5)

When we take a census, we attempt to collect data from

c. every individual in the population

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?

c. it could be any number between $35,000 and $41,000

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

c. reduce the variability of the estimate

Which of the following random variables is geometric?

c. the number of digits I read in a randomly selected row of the random digits table until I find a 7

Which one of the following is true about the events "owner has a chevy" and " owner's truck has four-wheel drive"?

c. these two events are not mutually exclusive, but they are independent

A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over 1000 Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of 1 inch could be increased by

c. using level= 0.05 instead of a level= 0.01

You want to know the opinion of American High School teacher's 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 by 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 the situation is true?

d. the results of the survey may be affected by undercoverage and non-response

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. Which of the following best describes the design of this experiment?

d. this is a completely randomized design with two explanatory variables (factors)

Suppose that a student is randomly selected from a large high school. The probability that the student is a senior is 0.22. The probability that the student has a driver's license is 0.30. If the probability that the student is a senior or has a driver's license is 0.36, what is the probability that the student is a senior and has a driver's license?

e. 0.160

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 at most $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 which of the following?

d. 609

The Environmental Protection Agency (EPA) requires that the exhaust of each model of motor vehicle be tested for the level of several pollutants. The level of oxides of nitrogen (NOX) in the exhaust of one light truck model was found to vary among individual trucks according to an approximately Normal distribution with mean μ=1.45 grams per mile driven and standard deviation σ=0.40 gram per mile. Which of the following best estimates the proportion of light trucks of this model with NOX levels greater than 2 grams per mile?

b. 0.0846

The partially complete table that follows shows the distribution of scores on the AP® Statistics exam for a class of students. Select a student from this class at random. If the student earned a score of 3 or higher on the AP® Statistics exam, what is the probability that the student scored a 5?

b. 0.214

You want to compute a 90% confidence interval for the mean of a population with an unknown population standard deviation. The sample size is 30. What critical value should you use for this interval?

b. 1.699

What is the predicted increase in temperature for an increase of 5 chirps per minute?

b. 16.5 ℉

Rainwater was collected in water containers 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. What are the mean and standard deviation of the corrected pH measurements?

b. 5.64, 1.32

A researcher initially plans to take an SRS of size 160 from a certain population and calculate the sample mean x-bar. Later, the researcher decides to increase the sample size so that the standard deviation of the sampling distribution of x-bar will be half as big as when using a sample size of 160. What sample size should the researcher use?

d. 640

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?

c. 72%: is a statistic, 56%: is a parameter

A 90% confidence interval for the mean μ of a population is computed from a random sample and is found to be 90 ± 30. Which of the following could be the 95% confidence interval based on the same data?

c. 90 +/- 39

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 early 1990s was 470 and the standard deviation was 110. In 2016, the mean was 510 and the standard deviation was 103. Gina took the SAT in 1994 and scored 500. Her cousin Colleen took the SAT in 2016 and scored 530. Who did better on the exam, and how can you tell?

c. Gina, her standardized score is higher than Colleen's

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 14 from the population?

c. a boxplot shows that the values above the median are much more variable

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

c. it gave every possible sample of size 30 an equal chance to be selected

Which of the following is the correct way to perform the simulations?

c. let integers from 1 to 56 represent making a free throw and 57 to 100 represent missing a free throw. Generate 50 random integers from 1 to 100. Count the number of made free throws. Repeat this process many times.

Wilt is a fine basketball player, but his free-throw shooting could use some work. For the past three seasons, he has made only 56% of his free throws. His coach sends him to a summer clinic to work on his shot, and when he returns, his coach has him step to the free-throw line and take 50 shots. He makes 34 shots. Is this result convincing evidence that Wilt's free-throw shooting has improved? We want to perform a simulation to estimate the probability that a 56% free-throw shooter would make 34 or more in a sample of 50 shots. Which of the following is the correct way to perform the simulations?

c. let integers from 1 to 56 represent making a free throw and 57 to 100 represent missing a free throw. Generate 50 random integers from 1 to 100. Count the number of made free throws. Repeat this process many times.

Which of the following is most likely true?

c. mean > median, range > IQR

In a test of Null: p=0.4 against Alternative: p≠ 0.4, a random sample of size 100 yields a standardized test statistic of z= 1.28. Which of the following is closest to the P-value for this test?

d. 0.20

Let D be the difference in the number of puzzles solved by two randomly selected subjects in a 5-minute period. What is the standard deviation of D?

d. 1.27

Because a person with no lean body mass should burn no calories, it makes sense to model the relationship with a direct variation function in the form y = kx. Models were tried using different values of k (k = 25, k = 26, etc.) and the sum of squared residuals (SSR) was calculated for each value of k. Here is a scatterplot showing the relationship between SSR and k: According to the scatterplot, what is the ideal value of k to use for predicting metabolic rate?

d. 31

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

d. 40%

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 true proportion p of all 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?

d. 700

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?

d. We can't conclude that drugs prolong life because the groups might differ in ways besides the treatment

Bias in a sampling method is

d. 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

Researchers randomly selected 1700 people from Canada who had never suffered a heart attack and rated the happiness of each person. Ten years later, the researchers followed up with each person and found that people who were initially rated as happy were less likely to have a heart problem. Which of the following is the most appropriate conclusion based on this study?

d. happier people in Canada are less likely to have heart problems

Which of the following is not a correct statement about the results of this Experiment?

d. high and low concentrations of either chemical have approximately the same effect

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 randomly selected 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?

d. mu of y=$75 and sd of y= $22.50

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)?

d. random assignment will tend to average out all other uncontrolled factors such as fertility so that they are not confounded with the treatment effects

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?

d. we expect that the estimate from Ohio State will be closer to the truth than the estimate from Johns Hopkins because it comes from a larger population

The security system in a house has two units that set off an alarm when motion is detected. Neither one is entirely reliable, but one or both always go off when there is motion anywhere in the house. Suppose that for motion in a certain location, the probability that detector A goes off and detector B does not go off is 0.25, and the probability that detector A does not go off is 0.35. What is the probability that detector B goes off?

e. 0.75

Forty students took a statistics test worth 50 points. The dotplot displays the data. The third quartile is

e. 23

What percent of all small companies receiving questionnaires responded "yes"?

e. 62.5%

The scatterplot shows the relationship between the number of people per television set and the number of people per physician for 40 countries, along with the least-squares regression line. In Ethiopia, there were 503 people per TV and 36,660 people per doctor. Which of the following is correct?

e. Ethiopia has more people per doctor than expected, based on how many people it has per TV

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

e. Pete did better than about 73% of test-takers

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?

e. no; the margin of error only accounts for sampling variability

A 95% confidence interval for the proportion of viewers of a certain reality television show who are over 30 years old is (0.26, 0.35). Suppose the show's producers want to test the hypothesis Null: p= 0.25 against Alternative: p≠ 0.25. Which of the following is an appropriate conclusion for them to draw at the 0.05 significance level?

e. reject the null; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from 0.25

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

e. symmetric but not Normal

The standard deviation of the distribution of house age is about 16 years. Interpret this value.

e. the age of the houses in the sample ...

A significance test allows you to reject a null hypothesis in favor of an alternative hypothesis at the 5% significance level. What can you say about significance at the 1% level?

e. the answer can't be determined from the given information

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

e. the area between A & G is equal to one

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 20.44. We may conclude that

e. the correlation will also be -0.44

Which of the following statements about the sampling distribution of the sample mean is incorrect?

e. the sampling distribution shows how the sample is distributed around the sample mean

Suppose a student is randomly selected from your school. Which of the following pairs of random variables are most likely independent?

e. x= average amount of homework the student does per night; Y= student's height

You are thinking of conducting a one-sample t-test about a population mean mu using a 0.05 significance level. Which of the following statements is correct?

e. you can safely carry out the test if n>/= 30