AP Statistics Final
People with type O-negative blood are universal donors. That is, any patient can receive a transfusion of O-negative blood. Only 7.2% of the American population has O-negative blood. If 10 people appear at random to give blood, what is the probability that at least 1 of them is a universal donor?
C 0.526
What is the range of sample sizes a researcher could take from a population of 750 without violating conditions required for performing Normal calculations with the sampling distribution of x-bar?
C 30 <or= n <or= 75
We record data on the population of a particular country from 1960 to 2010. A scatterplot reveals a clear curved relationship between population and year. However, a different scatterplot reveals a strong linear relationship between the logarithm (base 10) of the population and the year. The least-squares regression line for the transformed data is: log(population) = -13.5 +0.01 (year) Based on this equation, the population of the country in the year 2020 should be about
C 5,000,000
A researcher studying reaction time of drivers states that, "A 95% confidence interval for the mean time it takes for a driver to apply the brakes after seeing the brake lights on a vehicle in front of him is 1.2 to 1.8 seconds. What are the point estimate and margin of error for this interval?
E Point estimate = 1.5 seconds; margin of error = 0.3 seconds.
If P(A) = 0.24 and P(B) = 0.52 and A and B are independent, what is P(A or B)?
c 0.6352
A researcher is interested in the cholesterol levels of adults in the city she lives in. A cholesterol-screening program is set up in the downtown area during the lunch hour. Individuals can walk in and have their cholesterol measured for no charge. In one lunch hour, 173 people use the service, and their average cholesterol level is 217.8. The sample obtained here is an example of
c a sample probably containing bias and undercoverage.
A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with that in a school district of a large city. The researcher obtained an SRS of 60 high school students in a large suburban school district and found the mean time spent in extracurricular activities per week to be 6 hours with a standard deviation of 3 hours. The researcher also obtained an independent SRS of 40 high school students in a large city school district and found the mean time spent in extracurricular activities per week to be 5 hours with a standard deviation of 2 hours. Suppose that the researcher decides to carry out a significance test of Ho: μ (suburban) = μ (city) versus a two-sided alternative. The correct test statistic is
(b)
A researcher plans to conduct a test of hypotheses at the 1% significance level. She designs her study to have a power of 0.92 at a particular alternative value of the parameter of interest. The probability that the researcher will commit a Type I error is
A 0.01
The incomes in a certain large population of college teachers have a normal distribution with mean $60,000 and standard deviation $5000. Four teachers are selected at random from this population to serve on a salary review committee. What is the probability that their average salary exceeds $65,000?
A 0.0228
The probability that you will be ticketed for illegal parking on campus is about 1/3. During the last nine days, you have illegally parked every day and have NOT been ticketed (you lucky person!). Today, on the 10th day, you again decide to park illegally. Assuming the outcomes are independent from day to day, the probability that you will be caught is
A 1/3
What effect will decreasing the value of μ and increasing the value of σ have on the appearance of a Normal density curve?
A. The peak will move to the left, and the curve will become shorter and broader.
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 (see picture). Which of the following statements is/are true?
A.One only I. If the student had used Calculator as the explanatory variable, the correlation would remain the same.
An agricultural researcher wants to compare the effect on yield of three different methods of growing blueberries. To control for variables such as soil condition and location, he plants 30 plots on each of six different farms. On each farm, 10 of the 30 plots are assigned to each of the three treatments (growing methods). The researcher measures and compares the marketable yield of blueberries produced by each plot. Which of the following best describes the design of this experiment?
B a randomized block design with six blocks and three treatments
A researcher in early childhood education believes that kindergarten-age children are more receptive to help from a female teacher than from a male teacher. From a list of kindergarten teachers in the state, the researcher randomly samples four classes with male teachers and four classes with female teachers. The students in the classes are interviewed, and a measure of how receptive the students in each class are to help from the teacher is determined. This study is an example of
B an observational study
According to the 1.5 x IQR rule, how many outliers are there in the data set 110, 144, 115, 123, 114, 118, 72, 156?
B one
Which of these 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.
An experiment to test the effectiveness of regular treatments with fluoride varnish to reduce tooth decay involved 36 volunteers who had half of their teeth—the right side or left side, determined by a coin flip—painted with a fluoride varnish every six month for 5 years. At the end of the treatments, the number of new cavities during the treatment period was compared on treatment (fluoride varnish) side versus the control (no fluoride varnish) side. The appropriate statistical test for analyzing the results of this experiment is
C One-sample t-test on paired data.
the stem-and-leaf diagram below gives the distribution of the ages in years of 20 participants at a family reunion. Which of the following statements about the distribution is correct?
C The mean is larger than the median.
In your top dresser drawer are 6 blue socks and 10 grey socks, unpaired and mixed up. One dark morning you pull two socks from the drawer (without replacement, of course!). What is the probability that the two socks match?
D 0.500
The weights of tomatoes chosen at random from a bin at the farmer's market is a random variable with mean m = 10 ounces and SD = 1 ounce. Suppose we pick four tomatoes at random from the bin and find their total weight T. The random variable T has a standard deviation (in ounces) of
D 2
The critical value used to construct a confidence interval for a proportion depends upon
Only on the confidence level.
What percentage of all students surveyed are conservatives majoring in business?
A 12.1%
A study was done to examine the personal goals of fourth-, fifth-, and sixth-grade children. Random samples of students were selected for each of these grades from schools in the state of Georgia. The students received a questionnaire regarding personal goals. They were asked what they would most like to do at school: get good grades, be popular, or be good at sports. The results are presented in the table, classified by the gender of the child. Suppose we wish to test the null hypothesis that there are no differences among the proportion of boys and the proportion of girls choosing each of the three personal goals. Under the assumption that H0 is true, the test statistic has a χ2 distribution with a number of degrees of freedom equal to
A 2
A study was done to examine the personal goals of fourth-, fifth-, and sixth-grade children. Random samples of students were selected for each of these grades from schools in the state of Georgia. The students received a questionnaire regarding personal goals. They were asked what they would most like to do at school: get good grades, be popular, or be good at sports. The results are presented in the table, classified by the gender of the child. Suppose we wish to test the null hypothesis that there are no differences among the proportion of boys and the proportion of girls choosing each of the three personal goals. Under the null hypothesis, the expected number of boys that would select "be good at sports" is
A 49.4
The lifetime of a 2-volt nonrechargeable battery in constant use has a Normal distribution with a mean of 516 hours and a standard deviation of 20 hours. Of all batteries, 90% have a lifetime shorter than
A 541.6 hours
The scores of individual students on a college entrance examination have a left-skewed distribution with mean 18.6 and standard deviation of 6.0. At Millard North High School, 36 seniors take the test. The sampling distribution of mean scores for random samples of 36 students is
A Approximately Normal
The power takeoff driveline on tractors used in agriculture is a potentially serious hazard to operators of farm equipment. The driveline is covered by a shield in new tractors, but for a variety of reasons, the shield is often missing on older tractors. Two types of shields are the bolt-on and the flip-up. It was believed that the bolt-on shield was perceived as a nuisance by the operators and deliberately removed, but the flip-up shield is easily lifted for inspection and maintenance and may be left in place. In a study initiated by the U.S. National Safety Council, random samples of older tractors with both types of shields were taken to see what proportion of shields were removed. Of 183 tractors designed to have bolt-on shields, 35 had been removed. Of the 136 tractors with flip-up shields, 9 were removed. We wish to perform a test of Ho: pb = pf versus Ha: pb ≠ pf where pb and pf are the proportions of all tractors with the bolt-on and flip-up shields removed, respectively. Which of the following conditions for performing the appropriate significance test is definitely NOT satisfied in this case?
A Both populations are Normally distributed.
Event A occurs with probability 0.2. Event B occurs with probability 0.8. If A and B are disjoint (mutually exclusive), then
A P(A or B) = 1.0.
The variability of a statistic is described by
A The spread of its sampling distribution
A fast-talking salesman offers you a table of "random digits" that comes with a "guarantee" of randomness. You don't trust him, so you insist on testing the table by generating a sample of 300 digits from its rows. Here are the resulting frequencies of the 10 digits 0 through 9 in your sample of size 300 (see table). With the salesman getting more nervous by the minute, you then conduct a goodness-of-fit test of the null hypothesis that the table's digits are indeed random (that is, that the probability of seeing any of the 10 digits 0 through 9 in a single observation is equal to 1/10 or 0.10) against the alternative that they are not random. What do you conclude?
A There is no reason to doubt that the table's digits are indeed random: the P-value of the test is greater than 0.10.
A quiz question gives random samples of n = 10 observations from each of two Normally distributed populations. Tom uses a table of t distribution critical values and 9 degrees of freedom to calculate a 95% confidence interval for the difference in the two population means. Janelle uses her calculator's two-sample t interval with 16.87 degrees of freedom to compute the 95% confidence interval. Assume that both students calculate the intervals correctly. Which of the following is true?
A Tom's confidence interval is wider.
A study involving overweight, postmenopausal women aged 50 to 75 randomly assigned equal numbers of women to an exercise program (at least 45 minutes of moderate walking or riding an exercise bike five times a week) and to a stretching program (15 to 30 minutes of stretching three times a week, under the supervision of an exercise physiologist). It was found that a higher percentage of women in the exercise group reported improved sleep than did women in the stretching group. This study is an example of
A an experiment, but not a double-blind experiment.
A study covering many countries found a strong positive correlation between the life expectancy in a country and the percentage of households in the country with telephones. The best explanation of this observed correlation is that
A both life expectancy and telephone ownership are exhibiting a common response to the lurking variable of the country's socioeconomic condition.
If we reject the null hypothesis when, in fact, it is true, we have
A committed a Type I error
In a test of significance, the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as the value actually observed is
A the P-value of the test
An old saying in golf is "You drive for show and you putt for dough." The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour's world money list are examined. The average number of putts per hole and the player's total winnings for the previous season are recorded. A least-squares regression line was fitted to the data. The following results were obtained from statistical software. The correlation between total winnings and average number of putts per hole for these players is
A −0.285.
Thirty-five people from a random sample of 125 workers from Company A admitted to using sick leave when they weren't really ill. Seventeen employees from a random sample of 68 workers from Company B admitted that they had used sick leave when they weren't ill. A 95% confidence interval for the difference in the proportions of workers at the two companies who would admit to using sick leave when they weren't ill is
B (b)
The time it takes students to complete a statistics quiz has a mean of 20.5 minutes and a standard deviation of 15.4 minutes. What is the probability that a random sample of 40 students will have a mean completion time greater than 25 minutes?
B 0.0322
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
You select one student from this group at random. If the student says he is a junior, what is the probability that he walks to school?
B 0.160
A psychologist studied the number of puzzles that subjects were able to solve in a five-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a subject. The psychologist found that X had the following probability distribution (see table). What is the probability that a randomly chosen subject completes at least 3 puzzles in the five-minute period while listening to soothing music?
B 0.4
Scores on the American College Testing (ACT) college entrance exam follow a Normal distribution with mean 18 and standard deviation 6. Lisa's standardized score on the ACT was z = -0.7. What was her actual ACT score?
B 13.8
The median of the distribution is located in the class from
B 14 up to but not including 16
A sample of 20 is selected from the population. To determine the appropriate critical t-value what number of degrees of freedom should be used?
B 19
What percentage of liberals surveyed were humanities majors?
B 35.2%
A company that manufactures and bottles apple juice has a machine that automatically fills 16-ounce bottles. There is some variation, however, in the exact amount of juice dispensed into each bottle. From a large number of observations taken over a long period of time, it was found that the actual amount of juice dispensed into each bottle was Normally distributed with a mean of 16 ounces and a standard deviation of 1 ounce. Find the percentage of all bottles that are either underfilled or overfilled by at least 0.25 ounce.
B 80.26%
A chi-square goodness-of-fit test is used to test whether a 0 to 9 spinner is "fair" (that is, the outcomes are all equally likely). The spinner is spun 100 times, and the results are recorded. The degrees of freedom for the test will be
B 9
Which of the following confidence intervals has the largest critical value?
B A 95% t-interval with 1 degree of freedom
The mean area, mu, of the several thousand apartments in a new development is advertised to be 1200 square feet. A tenant group thinks that the apartments are smaller than advertised. They hire an engineer to measure a sample of apartments to test their suspicion. The null and alternative hypotheses, Ho and Ha, for an appropriate test of hypotheses are
B Ho: mu = 1200 Ha: mu < 1200
According to a recent poll, 27% of Americans prefer to read their news in a physical newspaper instead of online. Let's assume this is the parameter value for the population. If you take a simple random sample of 25 Americans and let p-hat be the proportion in the sample who prefer a newspaper, is the shape of the sampling distribution of p-hat approximately Normal?
B No, because np = 6.75
Which of the following statements about the chi-square (χ2) distribution is true?
B The distributions are only positive values, and will be skewed right
You select one student from this group at random. Which of the following statement is true about the events "Typically walks to school" and "Junior?"
B The events are not mutually exclusive but they are independent.
How much more effective is exercise and drug treatment than drug treatment alone at reducing the rate of heart attacks among men aged 65 and older? To find out, researchers perform a completely randomized experiment involving 1000 healthy males in this age group. Half of the subjects are assigned to receive drug treatment only, while the other half are assigned to exercise regularly and to receive drug treatment. The most appropriate inference method for answering the original research question is
B two-sample z interval for p1 − p2.
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?
C (c)
Eighty rats whose mothers were exposed to high levels of tobacco smoke during pregnancy were put through a simple maze. The maze required the rats make a choice between going left or going right at the outset. Sixty of the rats went right when running the maze for the first time. Assume that the eighty rats can be considered an SRS from the population of all rats born to mothers exposed to high levels of tobacco smoke during pregnancy. (Note that this assumption may or may not be reasonable, but researchers often assume lab rats are representative of such larger populations because lab rats are often bred to have very uniform characteristics.) The standard error for the proportion p of those who went right the first time when running the maze is
C 0.0484
A newspaper conducted a statewide survey concerning the 2008 race for state senator. The newspaper took a random sample (assume it is an SRS) of 1200 registered voters and found that 620 would vote for the Republican candidate. Let p represent the proportion of registered voters in the state that would vote for the Republican candidate. A 90% confidence interval for p is
C 0.517 ± 0.024.
The heights (in inches) of males in the United States are believed to be Normally distributed with mean μ. The average height of a random sample of twenty-five American adult males is found to be J = 69.72 inches and the standard deviation of the twenty-five heights is found to be s = 4.15. The standard error of J is
C 0.83
Twelve people who suffer from chronic fatigue syndrome volunteer to take part in an experiment to see if shark-fin extract will increase energy level. Eight of the volunteers are men, and four are women. Half of the volunteers are to be given shark-fin extract twice a day and the other half a placebo twice a day. We want to make sure that four men and two women are assigned to each treatment, so we decide to use a block design, with the men forming one block and the women the other. The names of the men and women are given in the chart, and each name is given the indicated single-digit numerical label. Use the list of random digits to assign four men and two women to the shark-fin treatment group. Read the table, starting at the beginning of the first line, from left to right, first selecting the four men and then the two women. According to this scheme, the subjects assigned to the shark-fin treatment are
C Lewis, Simpson, Howard, Adams, Braun, and Miller.
An agricultural researcher plants 25 plots with a new variety of corn. A 90% confidence interval for the average yield for these plots is found to be 162.72 ± 4.47 bushels per acre. Which of the following would produce a confidence interval with a smaller margin of error than this one?
C Planting 100 plots, rather than 25.
At a baseball game, 42 of 65 randomly selected people report owning an iPod. At a rock concert occurring at the same time across town, 34 of 52 randomly selected people report owning an iPod. A researcher wants to test the claim that the proportion of iPod owners at the two venues is different. A 90% confidence interval for the difference in population proportions is (−0.154, 0.138). Which of the following gives the correct outcome of the researcher's test of the claim?
C Since the confidence interval includes 0, the researcher cannot conclude that the proportion of iPod owners at the two venues is different.
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?
C Slope would decrease; y intercept would increase.
A sample was taken of the salaries of employees at a large company. Following are the salaries (in thousands of dollars) earned by 20 employees this past year. Suppose each employee in the company receives a $3000 raise for next year (that is, each employee's salary is increased by $3000). Which of the following will then occur?
C The interquartile range (IQR) will remain unchanged.
Which of the following is NOT one of the conditions that must be satisfied in order to perform inference about the slope of a least-squares regression line?
C The sample size—that is, the number of paired observations (x, y) — exceeds 30.
The fraction of the variation in the values of y that is explained by the least-squares regression of y on x is the
C correlation coefficient.
A study was conducted to determine whether or not there was a relationship between a child's birth order and her chances of becoming a juvenile delinquent. The subjects were a random sample of girls enrolled in public high schools in a large city. Each subject filled out a questionnaire that measured whether she had shown evidence of delinquent behavior, as well as her birth order. The resulting data are given in the table. What is the appropriate null hypothesis for this situation?
C delinquent behavior and birth order are independent.
Which of the following best describes replication in an experimental design?
C doubling the number of subjects or units in each treatment group
A 95% confidence interval for the mean μ of a population is computed from a random sample and found to be 9 ± 3. We may conclude that
C if we took many, many additional random samples and from each computed a 95% confidence interval for μ, approximately 95% of these intervals would contain μ.
You would like to compare the level of mathematical knowledge among 15-year-olds in the United States and Japan. To do this, you plan to give a mathematics achievement test to random samples of 1000 15-year-olds in each of the two countries. To ensure that the samples will include individuals from all different socioeconomic groups and educational backgrounds, you will randomly select 200 students from low-income families, 400 students from middle-income families, and 400 students from high-income families in each country. The sampling procedure being used here is
C stratified sampling.
An old saying in golf is "You drive for show and you putt for dough." The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69 of the nearly 1000 players on the PGA Tour's world money list are examined. The average number of putts per hole and the player's total winnings for the previous season are recorded. A least-squares regression line was fitted to the data. The following results were obtained from statistical software. Suppose that the researchers test the hypotheses H0 : β = 0, Ha : β < 0. The value of the t statistic for this test is
D -2.44
The weights of tomatoes chosen at random from a bin at the farmer's market is a random variable with mean m = 10 ounces and SD = 1 ounce. Suppose we pick four tomatoes at random from the bin and find their total weight T. The random variable T has a mean of
D 40 ounces
Suppose that three randomly selected subjects solve puzzles for five minutes each. The expected value of the total number of puzzles solved by the three subjects is
D 6.9
An SRS of 100 postal employees found that the average time these employees had worked for the postal service was J = 7 years with standard deviation s = 2 years. Assume the distribution of the time the population of employees have worked for the postal service is approximately Normal. A 95% confidence interval for the mean time μ the population of postal service employees have spent with the postal service is
D 7 ± 0.4.
Which of the following would provide evidence that a power model of the form y = axb, where b ≠ 0 and b ≠ 1, describes the relationship between a response variable y and an explanatory variable x?
D A scatterplot of ln y versus ln x looks approximately linear.
A test of significance produces a P-value of 0.0133. Which of the following conclusions are appropriate?
D Reject Ho at the α = 0.05 level
Inference about the slope β of a least-squares regression line is based on which of the following distributions?
D The t distribution with n − 2 degrees of freedom
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
D There is no linear relationship between number of activities and grade point average for students at this school.
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?
D μY = $75, σY = $22.50
Of people who died in the United States in a recent year, 86% were white, 12% were black, and 2% were Asian. (We will ignore the small number of deaths among other races.) Diabetes caused 2.8% of deaths among whites, 4.4% among blacks, and 3.5% among Asians. The probability that a randomly chosen death was due to diabetes is about
E 0.03
A significance test of the hypothesis Ho: p = 0.3 against the alternative Ha: p > 0.3 found a value of p-hat = 0.35 for a random sample of size 95. What is the P-value of this test?
E 0.1568
A marketing company discovered the following problems with a recent poll: I. Some people refused to answer questions II. People without telephones could not be in the sample III. Some people never answered the phone in several calls. Which of these sources is included in the ±2% margin of error announced for the poll?
E None of these are sources of error
A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with that in a school district of a large city. The researcher obtained an SRS of 60 high school students in a large suburban school district and found the mean time spent in extracurricular activities per week to be 6 hours with a standard deviation of 3 hours. The researcher also obtained an independent SRS of 40 high school students in a large city school district and found the mean time spent in extracurricular activities per week to be 5 hours with a standard deviation of 2 hours. Suppose that the researcher decides to carry out a significance test of Ho: μ (suburban) = μ (city) versus a two-sided alternative. The P-value for the test is 0.048. A correct conclusion is to
E reject Ho at the α = 0.05 level. There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.