Questions and Answers of Practice of Statistics

Find the unemployment rate for people with each level of education. Is there an association between unemployment rate and education? Explain your answer.In the language of government statistics, you
Each month the government releases unemployment statistics. The stated unemployment rate doesn’t include people who choose not to be employed, such as retirees. Based on a random sample of 1000
People love living in California for many reasons, but traffic isn’t one of them. Based on a random sample of 572 employed California adults, a 90% confidence interval for the average travel time
Refer to Exercise 6.a. Explain what would happen to the length of the interval if the confidence level was decreased to 90%.b. How would a 95% confidence interval based on triple the sample size
Refer to Exercise 5.a. Explain what would happen to the length of the interval if the confidence level were increased to 99%.b. How would a 95% confidence interval based on double the sample size
The admissions director for a university found that (107.8, 116.2) is a 95% confidence interval for the mean IQ score of all freshmen. Discuss whether each of the following explanations is correct,
A 95% confidence interval for the mean body mass index (BMI) of young American women is 26.8 ± 0.6. Discuss whether each of the following explanations is correct, based on that information.a. We are
The figure shows the result of taking 25 SRSs from a Normal population and constructing a confidence interval for the population mean using each sample. Which confidence level —80%, 90%, 95%, or
The figure shows the result of taking 25 SRSs from a Normal population and constructing a confidence interval for the population mean using each sample. Which confidence level —80%, 90%, 95%, or
The 2015 American Community Survey estimated the median household income for each state. According to ACS, the 90% confidence interval for the 2015 median household income in New Jersey is $72,222 ±
The 2015 American Community Survey estimated the median household income for each state. According to ACS, the 90% confidence interval for the 2015 median household income in Arizona is $51,492 ±
Refer to Exercise 6. Interpret the confidence level.Exercise 6.A Gallup poll asked a random sample of U.S. adults, “Would you like to lose weight?” Based on this poll, the 95% confidence interval
Refer to Exercise 5. Interpret the confidence level.Exercise 5.A New York Times/CBS News Poll asked a random sample of U.S. adults the question “Do you favor an amendment to the Constitution that
Many teens have posted profiles on sites such as Facebook. A sample survey asked random samples of teens with online profiles if they included false information in their profiles. Of 170 younger
The AP® Statistics class in Exercise 1 also asked an SRS of 20 boys at their school how many pairs of shoes they have. A 95% confidence interval for μG − μB = the true difference in the
A candy bar manufacturer sells a “fun size” version that is advertised to weigh 17 grams. A hungry teacher selected a random sample of 44 fun size bars and found a 95% confidence interval for the
A particular type of diet cola advertises that each can contains 12 ounces of the beverage. Each hour, a supervisor selects 10 cans at random, measures their contents, and computes a 95% confidence
A Gallup poll asked a random sample of U.S. adults, “Would you like to lose weight?” Based on this poll, the 95% confidence interval for the population proportion who want to lose weight is
A New York Times/CBS News Poll asked a random sample of U.S. adults the question “Do you favor an amendment to the Constitution that would permit organized prayer in public schools?” Based on
What proportion of students are willing to report cheating by other students? A student project put this question to an SRS of 172 undergraduates at a large university: “You witness two students
Tonya wants to estimate the proportion of seniors in her school who plan to attend the prom. She interviews an SRS of 50 of the 750 seniors in her school and finds that 36 plan to go to the prom.
The class in Exercise 1 wants to estimate the variability in the number of pairs of shoes that female students have by estimating the population standard deviation σ.Exercise 1.How many pairs of
How many pairs of shoes, on average, do female teens have? To find out, an AP® Statistics class selected an SRS of 20 female students from their school. Then they recorded the number of pairs of
Suppose that you randomly select one person 25 years of age or older.a. What is the probability that a randomly chosen person 25 years of age or older is in the labor force?b. If you know that a
The number of hours a lightbulb burns before failing varies from bulb to bulb. The population distribution of burnout times is strongly skewed to the right. The central limit theorem says that a. as
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
Why is it important to check the 10% condition before calculating probabilities involving x¯?a. To reduce the variability of the sampling distribution of x¯b. To ensure that the distribution of x¯
The distribution of scores on the mathematics part of the SAT exam in a recent year was approximately Normal with mean 515 and standard deviation 114. Imagine choosing many SRSs of 100 students who
The number of lightning strikes on a square kilometer of open ground in a year has mean 6 and standard deviation 2.4. The National Lightning Detection Network (NLDN) uses automatic sensors to watch
In response to the increasing weight of airline passengers, the Federal Aviation Administration (FAA) told airlines to assume that passengers average 190 pounds in the summer, including clothes and
Asked what the central limit theorem says, a student replies, “As you take larger and larger samples from a population, the variability of the sampling distribution of the sample mean decreases.”
Asked what the central limit theorem says, a student replies, “As you take larger and larger samples from a population, the histogram of the sample values looks more and more Normal.” Is the
A study of rush-hour traffic in San Francisco counts the number of people in each car entering a freeway at a suburban interchange. Suppose that this count has mean 1.6 and standard deviation 0.75 in
The number of flaws per square yard in a type of carpet material varies with mean 1.6 flaws per square yard and standard deviation 1.2 flaws per square yard.a. Without doing any calculations, explain
At a traveling carnival, a popular game is called the “Cash Grab.” In this game, participants step into a sealed booth, a powerful fan turns on, and dollar bills are dropped from the ceiling. A
An insurance company claims that in the entire population of homeowners, the mean annual loss from fire is μ = $250 and the standard deviation of the loss is σ = $5000. The distribution of losses
The distribution of grade point average for students at a large high school is skewed to the left with a mean of 3.53 and a standard deviation of 1.02.a. Describe the shape of the sampling
David’s iPod has about 10,000 songs. The distribution of the play times for these songs is heavily skewed to the right with a mean of 225 seconds and a standard deviation of 60 seconds.a. Describe
The manufacturer of a certain brand of aluminum foil claims that the amount of foil on each roll follows a Normal distribution with a mean of 250 square feet (ft2) and a standard deviation of 2 ft2.
A car company claims that the lifetime of its batteries varies from car to car according to a Normal distribution with mean μ = 48 months and standard deviation σ = 8.2 months. A consumer
One dimension of bird beaks is “depth”—the height of the beak where it arises from the bird’s head. During a research study on one island in the Galapagos archipelago, the beak depth of all
Suppose that the blood cholesterol level of all men aged 20 to 34 follows the Normal distribution with mean μ = 188 milligrams per deciliter (mg/dl) and standard deviation σ = 41 mg/dl.a. Choose an
A company’s cereal boxes advertise that each box contains 9.65 ounces of cereal. In fact, the amount of cereal in a randomly selected box follows a Normal distribution with mean μ = 9.70 ounces
A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed to contain 300 milliliters (ml). In fact, the contents vary according to a Normal distribution
Refer to Exercise 54. How many axles would you need to sample if you wanted the standard deviation of the sampling distribution of x̅ to be 0.0005 mm? Justify your answer.
Refer to Exercise 53. How many songs would you need to sample if you wanted the standard deviation of the sampling distribution of x̅ to be 10 seconds? Justify your answer.Exercise 53.David’s iPod
A grinding machine in an auto parts plant prepares axles with a target diameter μ = 40.125 millimeters (mm). The machine has some variability, so the standard deviation of the diameters is σ =
David’s iPod has about 10,000 songs. The distribution of the play times for these songs is heavily skewed to the right with a mean of 225 seconds and a standard deviation of 60 seconds. Suppose we
A series of observational studies revealed that people who typically consume 3 servings of whole grain per day have about a 20% lower risk of dying from heart disease and about a 15% lower risk of
A sample survey reports that 29% of Internet users download music files online, 21% share music files from their computers, and 12% both download and share music.a. Make a two-way table that displays
The sampling distribution of p̂ is approximately Normal becausea. There are at least 7500 Division I college athletes.b. np = 225 and n(1 − p) = 525 are both at least 10.c. A random sample was
Which of the following are the mean and standard deviation of the sampling distribution of the sample proportion p̂?a. Mean = 0.30, SD = 0.017b. Mean = 0.30, SD = 0.55c. Mean = 0.30, SD = 0.0003d.
In a congressional district, 55% of the registered voters are Democrats. Which of the following is equivalent to the probability of getting less than 50% Democrats in a random sample of size
Decreasing the sample size from 750 to 375 would multiply the standard deviation bya. 2. b. √2 c. 1/2.(d)1/√2.(e) none of these.The magazine Sports Illustrated asked a random sample of
A hospital claims that 75% of people who come to its emergency room are seen by a doctor within 30 minutes of checking in. To verify this claim, an auditor inspects the medical records of 55 randomly
The design of an electronic circuit for a toaster calls for a 100-ohm resistor and a 250-ohm resistor connected in series so that their resistances add. The resistance X of a 100-ohm resistor in a
Refer to Exercise 49. At the main campus, full-time students pay $50 per unit. At the downtown campus, fulltime students pay $55 per unit. Find the mean of the difference D (Main − Downtown) in the
Mr. Shrager does not always let his statistics class out on time. In fact, he seems to end class according to his own “internal clock.” The density curve here models the distribution of Y, the
A mail-order company advertises that it ships 90% of its orders within three working days. You select an SRS of 100 of the 5000 orders received in the past week for an audit. The audit reveals that
Harley-Davidson motorcycles make up 14% of all the motorcycles registered in the United States. You plan to interview an SRS of 500 motorcycle owners. How likely is your sample to contain 20% or more
Suppose that 70% of college women have been on a diet within the past 12 months. A sample survey interviews an SRS of 267 college women. What is the probability that 75% or more of the women in the
In the game of Scrabble, each player begins by drawing 7 tiles from a bag containing 100 tiles. There are 42 vowels, 56 consonants, and 2 blank tiles in the bag. Cait chooses an SRS of 7 tiles. Let
The Gallup Poll asked a random sample of 1785 adults if they attended church during the past week. Let p̂ be the proportion of people in the sample who attended church. A newspaper report claims
A USA Today poll asked a random sample of 1012 U.S. adults what they do with the milk in the bowl after they have eaten the cereal. Let p^ be the proportion of people in the sample who drink the
The Transportation Security Administration (TSA) is responsible for airport safety. On some flights, TSA officers randomly select passengers for an extra security check before boarding. One such
What sample size would be required to reduce the standard deviation of the sampling distribution to one-third the value you found in Exercise 36(b)? Justify your answer.
What sample size would be required to reduce the standard deviation of the sampling distribution to one-half the value you found in Exercise 35(b)? Justify your answer.
A factory employs 3000 unionized workers, 90% of whom are male. A random sample of 15 workers is selected for a survey about worker satisfaction. Let p̂ = the proportion of males in the sample.a.
The makers of Skittles claim that 20% of Skittles candies are orange. Suppose this claim is true. You select a random sample of 30 Skittles from a large bag. Let p̂ = the proportion of orange
According to a recent U.S. Bureau of Labor Statistics report, the proportion of married couples with children in which both parents work outside the home is 59%.6 You select an SRS of 50 married
In a congressional district, 55% of registered voters are Democrats. A polling organization selects a random sample of 500 registered voters from this district. Let p̂ = the proportion of Democrats
Animal species produce more offspring when their supply of food goes up. Some animals appear able to anticipate unusual food abundance. Red squirrels eat seeds from pinecones, a food source that
The math department at a small school has 5 teachers. The ages of these teachers are 23, 34, 37, 42, and 58. Suppose you select a random sample of 4 teachers and calculate the sample minimum age.
Increasing the sample size of an opinion poll will reduce thea. Bias of the estimates made from the data collected in the poll.b. Variability of the estimates made from the data collected in the
In a residential neighborhood, the median value of a house is $200,000. For which of the following sample sizes is the sample median most likely to be above $250,000?a. n = 10b. n = 50c. n = 100d. n
Osteoporosis is a condition in which the bones become brittle due to loss of minerals. To diagnose osteoporosis, an elaborate apparatus measures bone mineral density (BMD). BMD is usually reported in
A statistic is an unbiased estimator of a parameter whena. the statistic is calculated from a random sample.b. in a single sample, the value of the statistic is equal to the value of the parameter.c.
At a particular college, 78% of all students are receiving some kind of financial aid. The school newspaper selects a random sample of 100 students and 72% of the respondents say they are receiving
The figure shows approximate sampling distributions of 4 different statistics intended to estimate the same parameter.a. Which statistics are unbiased estimators? Justify your answer.b. Which
List all 4 possible SRSs of size n = 3, calculate the minimum age for each sample, and display the sampling distribution of the sample minimum on a dotplot with the same scale as the dotplot in
A polling organization plans to ask a random sample of likely voters who they plan to vote for in an upcoming election. The researchers will report the sample proportion p̂ that favors the incumbent
List all 6 possible SRSs of size n = 2, calculate the proportion of red cars in the sample, and display the sampling distribution of the sample proportion on a dotplot. Is the sample proportion an
A study of the health of teenagers plans to measure the blood cholesterol levels of an SRS of 13- to 16-yearolds. The researchers will report the mean x̅ from their sample as an estimate of the mean
List all 4 possible SRSs of size n = 3, calculate the proportion of red cars in the sample, and display the sampling distribution of the sample proportion on a dotplot with the same scale as the
List all 6 possible SRSs of size n = 2, calculate the minimum age for each sample, and display the sampling distribution of the sample minimum on a dotplot. Is the sample minimum an unbiased
The dotplot shows the results of taking 300 SRSs of 10 temperature readings from a Normal population with μ = 50 and σ = 3 and recording the sample minimum each time. Suppose that the minimum of an
To see if the claim made in Exercise 12 is true at their high school, an AP® Statistics class chooses an SRS of twenty 16- year-old females at the school and measures their heights. In their sample,
The dotplot shows the results of taking 300 SRSs of 10 temperature readings from a Normal population with μ = 50 and σ = 3 and recording the sample standard deviation sx each time. Suppose that the
Refer to Exercises 12 and 14. Suppose that the sample mean height of the twenty 16-year-old females is x̅ = 65.8 inches. Would this sample mean provide convincing evidence that the average height of
Refer to Exercises 11 and 13. Suppose that the sample proportion of students who did all their assigned homework last week is p̂ = 57/100 = 0.57. Would this sample proportion provide convincing
Some skeptical AP® Statistics students want to investigate the newspaper’s claim in Exercise 11, so they choose an SRS of 100 students from the school to interview.In their sample, 45 students
A school newspaper article claims that 60% of the students at a large high school completed their assigned homework last week. Assume that this claim is true for the 2000 students at the school.a.
According to the National Center for Health Statistics, the distribution of height for 16-year-old females is modeled well by a Normal density curve with mean μ = 64 inches and standard deviation σ
List all 10 possible SRSs of size n = 3, calculate the median quiz score for each sample, and display the sampling distribution of the sample median on a dotplot.The small population of 5 students in
List all 10 possible SRSs of size n = 2, calculate the proportion of females for each sample, and display the sampling distribution of the sample proportion on a dotplot.The small population of 5
List all 10 possible SRSs of size n = 3, calculate the minimum quiz score for each sample, and display the sampling distribution of the sample minimum on a dotplot.The small population of 5 students
A production run of ball bearings is supposed to have a mean diameter of 2.5000 centimeters (cm). An inspector chooses 100 bearings at random from the run. These bearings have mean diameter 2.5009 cm.
Tom is cooking a large turkey breast for a holiday meal. He wants to be sure that the turkey is safe to eat, which requires a minimum internal temperature of 165°F. Tom uses a thermometer to measure
List all 10 possible SRSs of size n = 2, calculate the mean quiz score for each sample, and display the sampling distribution of the sample mean on a dotplot.The small population of 5 students in the
On Tuesday, the bottles of Arizona Iced Tea filled in a plant were supposed to contain an average of 20 ounces of iced tea. Quality control inspectors selected 50 bottles at random from the day’s

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