AP Stat CWC Final Review
The probability that a new microwave oven will stop working in less than 2 years is 0.05. The probability that a new microwave oven is damaged during delivery and stops working in less than 2 years is 0.04. The probability that a new microwave oven is damaged during delivery is 0.10. Given that a new microwave oven is damaged during delivery, what is the probability that it stops working in less than 2 years?
0.40
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 ŷ = 25.2 + 3.3x 9 < x < 25, where x is the number of chirps per minute and ŷ is the estimated temperature in degrees Fahrenheit. What is the estimated increase in temperature that corresponds to an increase of 5 chirps per minute?
16.5 ° F
A recent report indicated that 90 percent of adults in a certain region actively try to include vegetables in their diet. A simulation was conducted that consisted of 50 trials with a population parameter of 0.9. Each trial consisted of a sample size of 10. The number of successes out of 10 was recorded, where success represented an adult trying to include vegetables in the diet. Five possible simulation results are shown. Which simulation is the best match to the one described?
50 dots on the far right with the scale 1-10
In a certain school district, students from grade 6 through grade 12 can participate in a school-sponsored community service activity. The following bar chart shows the relative frequencies of students from each grade who participate in the community service activity. Which of the following statements is supported by the bar chart?
Grade 12 had the least relative frequency of participating students.
To check the effect of cold temperature on the elasticity of two brands of rubber bands, one box of Brand A and one box of Brand B rubber bands are tested. Ten bands from the Brand A box are placed in a freezer for two hours and ten bands from the Brand B box are kept at room temperature. The amount of stretch before breakage is measured on each rubber band, and the mean for the cold bands is compared to the mean for the others. Is this a good experimental design?
No, because temperature is confounded with brand.
A city planner wants to estimate the proportion of city residents who commute to work by subway each day. A random sample of 30 city residents was selected, and 28 of those selected indicated that they rode the subway to work. Is it appropriate to assume that the sampling distribution of the sample proportion is approximately normal?
No, because the sample is not large enough to satisfy the normality conditions.
The student government at a high school wants to conduct a survey of student opinion. It wants to begin with a simple random sample of 60 students. Which of the following survey methods will produce a simple random sample?
Number the students in the official school roster. Use a table of random numbers to choose 60 students from this roster for the survey.
The following frequency table shows the responses from a group of college students who were asked to choose their favorite flavor of ice cream. FlavorFrequency Vanilla100 Chocolate65 Strawberry35 Mint chip45 Coffee30 Butter pecan25 Which of the following statements is not supported by the table?
One-half of the students chose vanilla or chocolate.
The continuous random variable N has a normal distribution with mean 7.5 and standard deviation 2.5. For which of the following is the probability equal to 0 ?
P(N=8)
An agronomist is an expert in soil management and crop production. A certain state hires an agronomist to investigate whether there is a linear relationship between a wheat stalk's height and the yield of wheat. The agronomist collected data and used the data to test the claim that there is a linear relationship at a significance level of α=0.05. The agronomist tested the following hypotheses. H0:β1=0Ha:β1≠0 The test yielded a p-value of 0.25. Which of the following is a correct conclusion about the claim?
The null hypothesis is not rejected because 0.25>0.050.25>0.05. There is not sufficient evidence to suggest that there is a linear relationship between a wheat stalk's height and its yield.
Which of the following questions about cars in a school parking lot will allow for the collection of a set of categorical data?
What are the colors of the cars in the lot?
A certain statistic dˆ is being used to estimate a population parameter D. The expected value of dˆ is not equal to D. What property does dˆ exhibit?
d^ is biased.
A golfer recorded the following scores for each of four rounds of golf: 86, 81, 87, 82. The mean of the scores is 84. What is the sum of the squared deviations of the scores from the mean?
∑(x−x¯)^2=(86−84)^2+(81−84)^2+(87−84)^2+(82−84)^2
Which of the following can be used to show a cause-and-effect relationship between two variables?
A controlled experiment
There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?
Approximately normal with mean $206,274 and standard deviation $3,788
In the design of a survey, which of the following best explains how to minimize response bias?
Carefully word and field-test survey questions.
A random sample of the costs of repair jobs at a large muffler repair shop produces a mean of $127.95. and a standard deviation of $24.03. If the size of this sample is 40, which of the following is an approximate 90 percent confidence interval for the average cost of a repair at this repair shop?
$127.95 ± $6.25
A complex electronic device contains three components, A, B, and C. The probabilities of failure for each component in any one year are 0.01, 0.03, and 0.04, respectively. If any one component fails, the device will fail. If the components fail independently of one another, what is the probability that the device will not fail in one year?
0.922
In a test of H0: μ = 8 versus Ha: μ ≠ 8, a sample of size of 220 leads to a p-value of 0.034. Which of the following must be true?
A 95% confidence interval for μ calculated from these data will not include μ = 8.
A chi-square test for homogeneity was conducted to investigate whether the four high schools in a school district have different absentee rates for each of four grade levels. The chi-square test statistic and p-value of the test were 19.02 and 0.025, respectively. Which of the following is the correct interpretation of the p-value in the context of the test?
Assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger.
A veterinarian keeps track of the types of animals treated by an animal clinic. The following distribution represents the percentages of animals the clinic has historically encountered. Animal type Dogs 61% Cats 22% Livestock 8% Birds 6% Other 3% If the animal clinic treats 230 animals in a month, how many of each animal type would be expected?
Dogs 140.3 Cats 50.6 Livestock 18.4 Birds 13.8 Other 6.9
A company claims it audits its employees' transactions based on their job level. For entry-level positions, the company claims that 50 percent get a basic audit, 30 percent get an enhanced audit, and 20 percent get a complete audit. The company tests this hypothesis using a random sample and finds χ2=0.771 with a corresponding p-value of 0.68. Assuming conditions for inference were met, which of the following is the correct interpretation of the p-value?
If the null hypothesis were true, there would be a 68 percent chance of obtaining a chi-square value of at least 0.771.
A bank surveyed all of its 60 employees to determine the proportion who participate in volunteer activities. Which of the following statements is true?
The bank does not need to use an inference procedure to determine the proportion of employees who participate in volunteer activities because the survey was a census of all employees.
Under which of the following conditions is it preferable to use stratified random sampling rather than simple random sampling?
The population can be divided into strata so that the individuals in each stratum are as much alike as possible.
The probability of winning a certain game is 0.5. If at least 70 percent of the games in a series of n games are won, the player wins a prize. If the possible choices for n are n=10, n=20, and n=100, which value of n should the player choose in order to maximize the probability of winning a prize?
n=10 only
As part of a class project at a large university, Amber selected a random sample of 12 students in her major field of study. All students in the sample were asked to report their number of hours spent studying for the final exam and their score on the final exam. A regression analysis on the data produced the following partial computer output. Amber wants to compute a 95 percent confidence interval for the slope of the least squares regression line in the population of all students in her major field of study. Assuming that conditions for inference are satisfied, which of the following gives the margin of error for the confidence interval?
(2.228) (0.745)
The XYZ Office Supplies Company sells calculators in bulk at wholesale prices, as well as individually at retail prices. Next year's sales depend on market conditions, but executives use probability to find estimates of sales for the coming year. The following tables are estimates for next year's sales. What profit does XYZ Office Supplies Company expect to make for the next year if the profit from each calculator sold is $20 at wholesale and $30 at retail.
$220,700
A company sells concrete in batches of 5 cubic yards. The probability distribution of X, the number of cubic yards sold in a single order for concrete from this company, is shown in the table below. The expected value of the probability distribution of X is 19.25 and the standard deviation is 5.76. There is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by Y = 75X - 100. What is the standard deviation of Y?
$432.00
Circuit boards are assembled by selecting 4 computer chips at random from a large batch of chips. In this batch of chips, 90 percent of the chips are acceptable. Let X denote the number of acceptable chips out of a sample of 4 chips from this batch. What is the least probable value of X?
0
A random sample of 500 people were classified by their ages into 3 age-groups: 29 years and younger, 30 to 64 years, and 65 years and older. Each person from the sample was surveyed about which of 4 major brands of cell phone they used. Their responses were compiled and displayed in a 3-by-4 contingency table. A researcher will use the data to investigate whether there is an association between cell phone brand and age-group. Which of the following is the appropriate test for the investigation?
A chi-square test of independence
A market researcher asked a group of men and women to choose their favorite color design from a sample of advertisements. The results are shown in the following table. Red with Black: M: 21 W:15 Green with Black: M: 15 W: 3 Yellow with Black: M: 8 W: 11 Red with Blue: M: 12 W: 31 Green with Blue: M: 31 W: 24 Yellow with Blue: M: 9 W: 16 Which of the following statements is not supported by the table?
For men, the number who chose a design with black was greater than the number who chose a design with blue.
Consider a data set of positive values, at least two of which are not equal. Which of the following sample statistics will be changed when each value in this data set is multiplied by a constant whose absolute value is greater than 1? I.The mean II.The median III.The standard deviation
I,II,III
Eliza plans on constructing a confidence interval for the slope of a regression line. She creates the residual plot shown to check the conditions for creating the interval. Which of the following conditions appear to be met based on the residual plot? I.The true relationship between x and y is linear. II.The standard deviation of y is constant for different levels of x. III.The value of 0 is contained in the confidence interval
II and II only
A local company is interested in supporting environmentally friendly initiatives such as carpooling among employees. The company surveyed all of the 200 employees at the downtown offices. Employees responded as to whether or not they own a car and to the location of the home where they live. The results are shown in the table below. Which of the following statements about a randomly chosen person from these 200 employees is true?
If the person owns a car, he or she is more likely to live elsewhere in the city than to live in the downtown area in the city.
At a manufacturing company for medical supplies, machines produce parts used in highly specialized lasers. Company researchers are testing a new machine designed to improve the precision of the parts. The null hypothesis is that the new machine does not improve the precision. For the researchers, the more consequential error would be that the new machine actually improves the precision, but the test does not detect the improvement. Which of the following should the researchers do to avoid the more consequential error?
Increase the significance level to increase the probability of a Type II error.
For a roll of a fair die, each of the outcomes 1, 2, 3, 4, 5, or 6 is equally likely. A red die and a green die are rolled simultaneously, and the difference of the outcomes (red - green) is computed. This is repeated for a total of 500 rolls of the pair of dice. Which of the following graphs best represents the most reasonable distribution of the differences?
Normal looking distribution with both negative and positive numbers
Peggy constructed the 95 percent confidence interval (4.8,5.2) to estimate the slope of a regression model for a set of bivariate data with 24 data values. Peggy claims that the width of the confidence interval will increase if a sample size of 30 is used, all other things remaining the same. Quincy claims that the width of the confidence interval will decrease if a sample size of 30 is used. Which statement is true about the claims made by Peggy and Quincy?
Quincy's claim is correct.
A polling firm is interested in surveying a representative sample of registered voters in the United States. The firm has automated its sampling so that random phone numbers within the United States are called. Each time a number is called, the procedure below is followed. • If there is no response or if an answering machine is reached, another number is automatically called. • If a person answers, a survey worker verifies that the person is at least 18 years of age. • If the person is not at least 18 years of age, no response is recorded, and another number is called. • If the person is at least 18 years of age, that person is surveyed. Some people claim the procedure being used does not permit the results to be extended to all registered voters. Which of the following is NOT a legitimate concern about the procedure being used?
Registered voters with unlisted telephone numbers may be underrepresented in the sample.
A nonprofit organization plans to hold a raffle to raise funds for its operations. A total of 1,000 raffle tickets will be sold for $1.00 each. After all the tickets are sold, one ticket will be selected at random and its owner will receive $50.00. The expected value for the net gain for each ticket is -$0.95. What is the meaning of the expected value in this context?
The ticket owners lose an average of $0.95 per raffle ticket.
A survey of 57 students was conducted to determine whether or not they held jobs outside of school. The two-way table above shows the number of students by employment status (job, no job), and class (juniors, seniors). Which of the following best describes the relationship between employment status and class?
There appears to be an association, since the proportion of juniors having jobs is much larger than the proportion of seniors having jobs.
In a test of the null hypothesis H0: µ = 10 against the alternative hypothesis Ha: µ > 10, a sample from a normal population produces a mean of 13.4. The z-score for the sample is 2.12 and the p-value is 0.017. Based on these statistics, which of the following conclusions could be drawn?
There is reason to conclude that µ > 10.
The residual plots from five different least squares regression lines are shown below. Which of the plots provides the strongest evidence that its regression line is an appropriate model for the data and is consistent with the assumptions required for inference for regression?
Very randomly scattered graph with no sort of pattern
In 2010, a medical research group reported the results of an experiment to evaluate the effectiveness of acupuncture to treat a chronic intestinal condition. A group of volunteers with the chronic intestinal condition agreed to participate in the experiment and be randomly assigned to either a true acupuncture treatment or a placebo treatment. The placebo treatment mimicked the application of acupuncture, but no needle penetrated the skin. Random assignment resulted in 78 subjects receiving acupuncture and 75 subjects receiving the placebo treatment. After receiving 6 treatments over the course of 3 weeks, patients were asked to report whether they had experienced a reduction in the chronic intestinal condition. The table summarizes the data from the study, with expected cell counts in parentheses. Which of the following is true about the chi-square test for homogeneity?
Volunteers with the chronic intestinal condition were randomly assigned to each treatment, so the independence condition has been met.
A random sample of 1,175 people in a certain country were asked whether they thought climate change was a problem. The sample proportion of those who think climate change is a problem was calculated, and a 95 percent confidence interval was constructed as (0.146,0.214). Which of the following is a correct interpretation of the interval?
We are 95 percent confident that the proportion of all people in the country who think climate change is a problem is between 0.146 and 0.214.
There are 1,000 golden delicious and 1,000 red delicious apples in a cooler. In a random sample of 75 of the golden delicious apples, 48 had blemishes. In a random sample of 75 of the red delicious apples, 42 had blemishes. Assume all conditions for inference have been met. Which of the following is closest to the interval estimate of the difference in the numbers of apples with blemishes (golden delicious minus red delicious) at a 98 percent level of confidence?
(−105,265)
The process of producing pain-reliever tablets yields tablets with varying amounts of the active ingredient. It is claimed that the average amount of active ingredient per tablet is at least 200 milligrams. The Consumer Watchdog Bureau tests a random sample of 70 tablets. The mean content of the active ingredient for this sample is 194.3 milligrams, while the standard deviation is 21 milligrams. What is the approximate p-value for the appropriate test?
0.012
A summer resort rents rowboats to customers but does not allow more than four people to a boat. Each boat is designed to hold no more than 800 pounds. Suppose the distribution of adult males who rent boats, including their clothes and gear, is normal with a mean of 190 pounds and standard deviation of 10 pounds. If the weights of individual passengers are independent, what is the probability that a group of four adult male passengers will exceed the acceptable weight limit of 800 pounds?
0.023
A manufacturer claims its Brand A battery lasts longer than its competitor's Brand B battery. Nine batteries of each brand are tested independently, and the hours of battery life are shown in the table below. Provided that the assumptions for inference are met, which of the following tests should be conducted to determine if Brand A batteries do, in fact, last longer than Brand B batteries?
A one-sided, two-sample t-test
Perchlorate is a chemical used in rocket fuel. People who live near a former rocket-testing site are concerned that perchlorate is present in unsafe amounts in their drinking water. Drinking water is considered safe when the average level of perchlorate is 24.5 parts per billion (ppb) or less. A random sample of 28 water sources in this area produces a mean perchlorate measure of 25.3 ppb. Which of the following is an appropriate alternative hypothesis that addresses their concern?
Ha : μ > 24.5
In order to make statistical inferences when testing a population proportion p, which of the following conditions verify that inference procedures are appropriate? I.The data are collected using a random sample or random assignment. II.The sample size is less than 10 percent of the population size. III.np0≥10 and n(1−p0)≥10 for sample size n and hypothesized proportion p0.
I, II, III
Two voting districts, C and M, were sampled to investigate voter opinion about tax spending. From a random sample of 100 voters in District C, 22 percent responded yes to the question "Are you in favor of an increase in state spending on the arts?" An independent random sample of 100 voters in District M resulted in 26 percent responding yes to the question. A 95 percent confidence interval for the difference (pc−pm) was calculated as −0.04±0.12. Which of the following is the best interpretation of the interval?
We are 95% confident that the difference in the proportions of all voters in districts C and M who favor an increase in state spending for the arts is between −0.16−0.16 and 0.08.
The mean and standard deviation of the sample data collected on continuous variable x are −0.25 and 0.03, respectively. The following table shows the relative frequencies of the data in the given intervals. Based on the table, do the data support the use of a normal model to approximate population characteristics?
Yes, because the distribution of relative frequencies is very close to the empirical rule for normal models.
When using a one-sample t-procedure to construct a confidence interval for the mean of a finite population, a condition is that the population size be at least 10 times the sample size. The reason for the condition is to ensure that
the degree of dependence among observations is negligible
In a population of bats living in a certain region, 30 percent have a wingspan greater than 10 inches. In a random sample of 80 bats living outside of the region, 20 had a wingspan greater than 10 inches. Consider a one-sample z-test to investigate whether there is evidence that the proportion of bats with a wingspan greater than 10 inches living outside the region is different from that of the bats living in the region. Which of the following is the correct test statistic?
z=(0.25−0.30)/√((0.30*0.70)/80)
At a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds. Which of the following is closest to the proportion of orders that are processed in less than 240 seconds?
0.17
Consider n pairs of numbers (x1,y1), (x2,y2), ..., and (xn, yn). The mean and standard deviation of the x-values are x̄ =5 and sx = 4, respectively. The mean and standard deviation of the y-values are ȳ = 10 and sy = 10 respectively. Of the following, which could be the least squares regression line?
ŷ = 8.5 + 0.3x
The manager of a public swimming pool wants to compare the effectiveness of two laundry detergents, Detergent A and Detergent B, in cleaning the towels that are used daily. As each dirty towel is turned in, it is placed into the only washing machine on the premises. When the washing machine contains 20 towels, the manager flips a coin to determine whether Detergent A or Detergent B will be used for that load. The cleanliness of the load of towels is rated on a scale of 1 to 10 by a person who does not know which detergent was used. The manager continues this experiment for many days. Which of the following best describes the manager's study?
A completely randomized design
The Physicians' Health Study, a large medical experiment involving 22,000 male physicians, attempted to determine whether aspirin could help prevent heart attacks. In this study, one group of about 11,000 physicians took an aspirin every other day, while a control group took a placebo. After several years, it was determined that the physicians in the group that took aspirin had significantly fewer heart attacks than the physicians in the control group. Which of the following statements explains why it would not be appropriate to say that everyone should take an aspirin every other day? I.The study included only physicians, and different results may occur in individuals in other occupations. II.The study included only males and there may be different results for females. III.Although taking aspirin may be helpful in preventing heart attacks, it may be harmful to some other aspects of health.
I, II, and III
The boxplots above summarize two data sets, A and B. Which of the I.following must be true? Set A contains more data than Set B. II.The box of Set A contains more data than the box of Set B. III.The data in Set A have a larger range than the data in Set B.
III Only
The distribution of the number of transactions per day at a certain automated teller machine (ATM) is approximately normal with a mean of 80 transactions and a standard deviation of 10 transactions. Which of the following represents the parameters of the distribution?
μ=80;σ=10