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business
business statistics in practice

Questions and Answers of Business Statistics In Practice

A beef rancher randomly sampled 42 cattle from her large herd to obtain a 95% confidence interval to estimate the mean weight of the cows in the herd. The interval obtained was (1010, 1321). If the
School A has 400 students and School B has 2700 students. A local newspaper wants to compare the distributions of SAT scores for the two schools.Which of the following would be the most useful for
Let X represent the outcome when a fair six-sided die is rolled. For this random variable, mX = 3.5 and sX = 1.71. If the die is rolled 100 times, what is the approximate probability that the total
An agricultural station is testing the yields for six different varieties of seed corn. The station has four large fields available, which are located in four distinctly different parts of the
The correlation between the heights of fathers and the heights of their (grownup) sons is r = 0.52, both measured in inches. If fathers’ heights were measured in feet instead, the correlation
A random sample of 200 New York State voters included 88 Republicans, while a random sample of 300 California voters produced 141 Republicans.Which of the following represents the 95% confidence
Which of the following is not a property of a binomial setting?(a) Outcomes of different trials are independent.(b) The chance process consists of a fixed number of trials, n.(c) The probability of
Mrs. Woods and Mrs. Bryan are avid vegetable gardeners. They use different fertilizers, and each claims that hers is the best fertilizer to use when growing tomatoes. Both agree to do a study using
The Environmental Protection Agency is charged with monitoring industrial emissions that pollute the atmosphere and water. So long as emission levels stay within specified guidelines, the EPA does
Which of the following is false?(a) A measure of center alone does not completely describe the characteristics of a set of data. Some measure of spread is also needed.(b) If the original measurements
A 96% confidence interval for the proportion of the labor force that is unemployed in a certain city is (0.07, 0.10). Which of the following statements about this interval is true?(a) The probability
A large toy company introduces a lot of new toys to its product line each year. The company wants to predict the demand as measured by y, first-year sales (in millions of dollars) using x, awareness
Final grades for a class are approximately Normally distributed with a mean of 76 and a standard deviation of 8. A professor says that the top 10% of the class will receive an A, the next 20% a B,
National Park rangers keep data on the bears that inhabit their park. Below is a histogram of the weights of 143 bears measured in a recent year.Which statement below is correct?(a) The median will
A random sample of size n will be selected from a population, and the proportion of those in the sample who have a Facebook page will be calculated.How would the margin of error for a 95%confidence
A scatterplot and a least-squares regression line are shown in the figure below. What effect does point P have on the slope of the regression line and the correlation?(a) Point P increases the slope
The following dotplots show the average high temperatures(in degrees Fahrenheit) for a sample of tourist cities from around the world. Both the January and July average high temperatures are
Suppose the null and alternative hypotheses for a significance test are defined as H0 : m = 40 Ha : m < 40 Which of the following specific values for Ha will give the highest power?(a) m = 38 (c) m =
A large university is considering the establishment of a schoolwide recycling program. To gauge interest in the program by means of a questionnaire, the university takes separate random samples of
Suppose the true proportion of people who use public transportation to get to work in the Washington, D.C., area is 0.45. In a simple random sample of 250 people who work in Washington, about how far
If we are interested in whether students at this high school are getting too little sleep, which of the following represents the appropriate null and alternative hypotheses?(a) H0 : m = 7.9 and Ha :
A researcher wants to determine whether or not a five-week crash diet is effective over a long period of time. A random sample of 15 dieters is selected.Each person’s weight is recorded before
Which of the following is the test statistic for the hypothesis test?(a) t =7.9 − 9 2.1!28(b) t =9 − 7.9 2.1!28(c) t =7.9 − 9Å2.1 28(d) t =7.9 − 9 2.1!27(e) t =9 − 7.9 2.1!27
Shortly before the 2012 presidential election, a survey was taken by the school newspaper at a very large state university. Randomly selected students were asked, “Whom do you plan to vote for in
A researcher wants to determine whether or not a five-week crash diet is effective over a long period of time. A random sample of 15 dieters is selected.Each person’s weight is recorded before
Starting in the 1970s, medical technology allowed babies with very low birth weight (VLBW, less than 1500 grams, or about 3.3 pounds) to survive without major handicaps. It was noticed that these
A nuclear power plant releases water into a nearby lake every afternoon at 4:51 p.m. Environmental researchers are concerned that fish are being driven away from the area around the plant. They
The Candy Shoppe assembles gift boxes that contain 8 chocolate truffles and 2 handmade caramel nougats. The truffles have a mean weight of 2 ounces with a standard deviation of 0.5 ounce, and the
An investor is comparing two stocks, A and B.She wants to know if over the long run, there is a significant difference in the return on investment as measured by the percent increase or decrease in
Distinguish between a parameter and a statistic.
Use the sampling distribution of a statistic to evaluate a claim about a parameter.
Distinguish among the distribution of a population, the distribution of a sample, and the sampling distribution of a statistic.
Determine whether or not a statistic is an unbiased estimator of a population parameter.
Describe the relationship between sample size and the variability of a statistic.
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 sampled 50 bottles at random from the day’s
On a New York–to–Denver flight, 8% of the 125 passengers were selected for random security screening before boarding. According to the Transportation Security Administration, 10% of passengers at
Healthy living(a) A random sample of 1000 people who signed a card saying they intended to quit smoking were contacted 9 months later. It turned out that 210 (21%) of the sampled individuals had not
The economy(a) Each month, the Current Population Survey interviews a random sample of individuals in about 60,000 U.S. households. One of their goals is to estimate the national unemployment rate.
Get your bearings A large container is full of ball bearings with mean diameter 2.5003 centimeters (cm).This is within the specifications for acceptance of the container by the purchaser. By chance,
Voters Voter registration records show that 41% of voters in a state are registered as Democrats. To test a random digit dialing device, you use it to call 250 randomly chosen residential telephones
Unlisted numbers A telemarketing firm in a large city uses a device that dials residential telephone numbers in that city at random. Of the first 100 numbers dialed, 48% are unlisted. This is not
How tall? A random sample of female college students has a mean height of 64.5 inches, which is greater than the 63-inch mean height of all adult American women.
Sampling distribution(a) List all 15 possible SRSs of size n = 2 from the population.Find the value of x– for each sample.(b) Make a graph of the sampling distribution of x–.Describe what you see.
Sampling distribution(a) List all 15 possible SRSs of size n = 2 from the population.Find the value of the range for each sample.(b) Make a graph of the sampling distribution of the sample range.
Doing homework A school newspaper article claims that 60% of the students at a large high school did all their assigned homework last week. Some skeptical AP® Statistics students want to investigate
Tall girls According to the National Center for Health Statistics, the distribution of heights for 16-year-old females is modeled well by a Normal density curve with mean m = 64 inches and standard
Doing homework Refer to Exercise 9.(a) Make a bar graph of the population distribution given that the newspaper’s claim is correct.(b) Sketch a possible graph of the distribution of sample data for
Tall girls Refer to Exercise 10.(a) Make a graph of the population distribution.(b) Sketch a possible dotplot of the distribution of sample data for the SRS of size 20 taken by the AP®Statistics
Cold cabin? The Fathom screen shot below shows the results of taking 500 SRSs of 10 temperature readings from a population distribution that is N(50, 3)and recording the sample variance s2x each
Cold cabin? The Fathom screen shot below shows the results of taking 500 SRSs of 10 temperature readings from a population distribution that is N(50, 3)and recording the sample minimum each time.(a)
A sample of teens A study of the health of teenagers plans to measure the blood cholesterol levels of an SRS of 13- to 16-year-olds. The researchers will report the mean x– from their sample as an
Predict the election 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 p^ that
A sample of teens Refer to Exercise 15. The sample mean x– is an unbiased estimator of the population mean m no matter what size SRS the study chooses.Explain to someone who knows nothing about
Predict the election Refer to Exercise 16. The sample proportion p^ is an unbiased estimator of the population proportion p no matter what size random sample the polling organization chooses. Explain
Bias and variability The figure below shows histograms of four sampling distributions of different statistics intended to estimate the same parameter.(a) Which statistics are unbiased estimators?
IRS audits The Internal Revenue Service plans to examine an SRS of individual federal income tax returns. The parameter of interest is the proportion of all returns claiming itemized deductions.
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 some sort of financial aid. Which of the following
A statistic is an unbiased estimator of a parameter when(a) 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
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 = 10(b) n = 50(c) n =
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
Increasing the sample size of an opinion poll will reduce the(a) bias of the estimates made from the data collected in the poll.(b) variability of the estimates made from the data collected in the
Dem bones (2.2) 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
Squirrels and their food supply (3.2) 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
Find the mean and standard deviation of the sampling distribution of a sample proportion p^. Check the 10%condition before calculating sp^.
Determine if the sampling distribution of p^ is approximately Normal.
If appropriate, use a Normal distribution to calculate probabilities involving p^.
How is the sampling distribution of p^ related to the binomial count X ?
The candy machine Suppose a large candy machine has 45% orange candies. Use Figures 7.11 and 7.12(pages 441 and 442) to help answer the following questions.(a) Would you be surprised if a sample of
The candy machine Suppose a large candy machine has 15% orange candies. Use Figure 7.13(page 442) to help answer the following questions.(a) Would you be surprised if a sample of 25 candies from the
The candy machine Suppose a large candy machine has 45% orange candies. Imagine taking an SRS of 25 candies from the machine and observing the sample proportion p^ of orange candies.(a) What is the
The candy machine Suppose a large candy machine has 15% orange candies. Imagine taking an SRS of 25 candies from the machine and observing the sample proportion p^ of orange candies.(a) What is the
Airport security The Transportation Security Administration(TSA) is responsible for airport safety.On some flights, TSA officers randomly select passengers for an extra security check before
Scrabble 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
Hispanic workers A factory employs 3000 unionized workers, of whom 30% are Hispanic. The 15-member union executive committee contains 3 Hispanics. What would be the probability of 3 or fewer
Studious athletes A university is concerned about the academic standing of its intercollegiate athletes.A study committee chooses an SRS of 50 of the 316 athletes to interview in detail. Suppose that
Do you drink the cereal milk? 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
Do you go to church? The Gallup Poll asked a random sample of 1785 adults whether they attended church during the past week. Let p^ be the proportion of people in the sample who attended church. A
Do you drink the cereal milk? 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.
Do you go to church? 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.
Students on diets A sample survey interviews an SRS of 267 college women. Suppose that 70% of college women have been on a diet within the past 12 months. What is the probability that 75% or more of
Who owns a Harley? 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
On-time shipping 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
Study finds that 67% of college students support efforts to “crack down on underage drinking.” Does this result hold at a large local college? To find out, college administrators survey an SRS of
Which of the following are the mean and standard deviation of the sampling distribution of the sample proportion p^ ?(a) Mean = 0.30, SD = 0.017(b) Mean = 0.30, SD = 0.55(c) Mean = 0.30, SD =
Decreasing the sample size from 750 to 375 would multiply the standard deviation by(a) 2. (c) 1/2. (e) none of these.(b) !2. (d) 1•!2.
The sampling distribution of p^ is approximately Normal because (a) 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
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 100?(a)
Sharing music online (5.2) 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.5 Make a
California’s endangered animals (4.1) The California Department of Fish and Game publishes a list of the state’s endangered animals. The reptiles on the list are given below.Desert tortoise
Find the mean and standard deviation of the sampling distribution of a sample mean x–. Check the 10% condition before calculating sx–.
Explain how the shape of the sampling distribution of x–is affected by the shape of the population distribution and the sample size.
If appropriate, use a Normal distribution to calculate probabilities involving x–.
Find the probability that a randomly chosen pregnant woman has a pregnancy that lasts for more than 270 days. Show your work.Suppose we choose an SRS of 6 pregnant women. Let x– = the mean
What is the mean of the sampling distribution of x–? Explain.
Compute the standard deviation of the sampling distribution of x–. Check that the 10% condition is met.
Find the probability that the mean pregnancy length for the women in the sample exceeds 270 days. Show your work.
Songs on an iPod 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
Making auto parts A grinding machine in an auto parts plant prepares axles with a target diameter m = 40.125 millimeters (mm). The machine has some variability, so the standard deviation of the
Making auto parts A grinding machine in an auto parts plant prepares axles with a target diameter m = 40.125 millimeters (mm). The machine has some variability, so the standard deviation of the
Making auto parts Refer to Exercise 50. How many axles would you need to sample if you wanted the standard deviation of the sampling distribution of x–to be 0.0005 mm? Justify your answer.

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