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business statistics in practice
Questions and Answers of
Business Statistics In Practice
Do Longer Drives Mean Lower Scores on the PGA Tour?
Check the conditions for performing inference about the slope b of the population (true) regression line.
Interpret the values ofa, b, s, SEb, and r 2 in context, and determine these values from computer output.
Construct and interpret a confidence interval for the slope b of the population (true) regression line.
Perform a significance test about the slope b of the population (true) regression line.
What’s with that formula for sb?
Beer and BA C Refer to Exercise 3. Computer output from the least-squares regression analysis on the beer and blood alcohol data is shown below.Dependent variable is: BAC No Selector R squared =
Prey attracts predators Refer to Exercise 4.Computer output from the least-squares regression analysis on the perch data is shown below.Predictor Coef Stdev. t-ratio p Constant 0.12049 0.09269 1.30
Beer and BA C Refer to Exercise 5.(a) Give the standard error of the slope, SEb. Interpret this value in context.(b) Find the critical value for a 99% confidence interval for the slope of the true
Prey attracts predators Refer to Exercise 6.(a) Give the standard error of the slope, SEb. Interpret this value in context.(b) Find the critical value for a 90% confidence interval for the slope of
Beavers and beetles Do beavers benefit beetles?Researchers laid out 23 circular plots, each 4 meters in diameter, at random in an area where beavers were cutting down cottonwood trees. In each plot,
Ideal proportions The students in Mr. Shenk’s class measured the arm spans and heights (in inches) of a random sample of 18 students from their large high school. Some computer output from a
Beavers and beetles Refer to Exercise 9.(a) How many clusters of beetle larvae would you predict in a circular plot with 5 tree stumps cut by beavers? Show your work.(b) About how far off do you
Ideal proportions Refer to Exercise 10.(a) What height would you predict for a student with an arm span of 76 inches? Show your work.(b) About how far off do you expect the prediction in part (a) to
Time at the table Does how long young children remain at the lunch table help predict how much they eat? Here are data on a random sample of 20 toddlers observed over several months.10 “Time”is
Is wine good for your heart? A researcher from the University of California, San Diego, collected data on average per capita wine consumption and heart disease death rate in a random sample of 19
The professor swims Here are data on the time (in minutes) Professor Moore takes to swim 2000 yards and his pulse rate (beats per minute) after swimming on a random sample of 23 days:Time: 34.12
The equation of the least-squares regression line for predicting selling price from appraised value is(a) price = 79.49 + 0.1126 (appraised value).(b) price = 0.1126 + 1.0466 (appraised value).(c)
The slope b of the population regression line describes(a) the exact increase in the selling price of an individual unit when its appraised value increases by $1000.(b) the average increase in the
Is there convincing evidence that selling price increases as appraised value increases? To answer this question, test the hypotheses(a) H0 : b = 0 versus Ha : b > 0.(b) H0 : b = 0 versus Ha : b <
Which of the following is the best interpretation for the value 0.1126 in the computer output?(a) For each increase of $1000 in appraised value, the average selling price increases by about
A 95% confidence interval for the population slope b is(a) 1.0466 ± 1.046. (d) 1.0466 ± 0.2207.(b) 1.0466 ± 0.2415. (e) 1.0466 ± 0.2400.(c) 1.0466 ± 0.2387.
Which of the following would have resulted in a violation of the conditions for inference?(a) If the entire sample was selected from one neighborhood(b) If the sample size was cut in half(c) If the
Color words (4.2) Let’s review the design of the study.(a) Explain why this was an experiment and not an observational study.(b) Did Mr. Starnes use a completely randomized design or a randomized
Color words (1.3) Do the data provide evidence of a difference in the average time required to perform the two tasks? Include an appropriate graph and numerical summaries in your answer.
Color words (9.3) Explain why it is not safe to use paired t procedures to do inference about the difference in the mean time to complete the two tasks.
Color words (3.1, 3.2, 12.1) Can we use a student’s word task time to predict his or her color task time?(a) Make an appropriate scatterplot to help answer this question. Describe what you see.(b)
Snowmobiles (5.2, 5.3)(a) If we choose a survey respondent at random, what’s the probability that this individual(i) is a snowmobile owner?(ii) belongs to an environmental organization or owns a
Snowmobiles (11.2) Do these data provide convincing evidence at the 5% significance level of an association between environmental club membership and snowmobile use for the population of visitors to
Use transformations involving powers and roots to find a power model that describes the relationship between two variables, and use the model to make predictions.
Use transformations involving logarithms to find a power model or an exponential model that describes the relationship between two variables, and use the model to make predictions.
Determine which of several transformations does a better job of producing a linear relationship.
The swinging pendulum Use your model from Exercise 35 to predict the period of a pendulum with length 80 centimeters. Show your work.
B oyle’s law Use your model from Exercise 36 to predict the pressure in the syringe when the volume is 17 cubic centimeters. Show your work.
Determining tree biomass It is easy to measure the “diameter at breast height” of a tree. It’s hard to measure the total “aboveground biomass” of a tree, because to do this you must cut and
45. Heart weights of mammals Here are some data on the hearts of various mammals.23 Mammal Length of cavity of left ventricle (cm) Heart weight (g)Mouse 0.55 0.13 Rat 1.0 0.64 Rabbit 2.2 5.8 Dog 4.0
Galileo’s experiment Galileo studied motion by rolling balls down ramps. He rolled a ball down a ramp with a horizontal shelf at the end of it so that the ball was moving horizontally when it
Suppose that the relationship between a response variable y and an explanatory variable x is modeled by y = 2.7(0.316)x. Which of the following scatterplots would approximately follow a straight
Some high school physics students dropped a ball and measured the distance fallen (in centimeters) at various times (in seconds) after its release. If you have studied physics, then you probably know
A scatterplot of x = Super Bowl number and y = cost of a 30-second advertisement on the Super Bowl broadcast (in dollars) shows a strong, positive, nonlinear association. A scatterplot of
A scatterplot of y versus x shows a positive, nonlinear association. Two different transformations are attempted to try to linearize the association: using the logarithm of the y values and using the
Shower time (1.3, 2.2, 6.3, 7.3) Marcella takes a shower every morning when she gets up. Her time in the shower varies according to a Normal distribution with mean 4.5 minutes and standard deviation
Tattoos (8.2, 9.2) Of the 98 teachers who responded, 23.5% said that they had one or more tattoos.(a) Construct and interpret a 95% confidence interval for the actual proportion of teachers at the
Tattoos (4.1) One of the first decisions the class had to make was what kind of sampling method to use.(a) They knew that a simple random sample was the“preferred” method. With 1100 teachers in
Casting aluminum(a) Describe what the scatterplot tells you about the relationship between cylinder wall thickness and gate velocity.(b) What is the equation of the least-squares regression line?
Casting aluminum Do the data provide convincing evidence at the a = 0.05 level of a linear relationship between thickness and gate velocity in the population of pistons formed from this alloy of
Casting aluminum Construct and interpret a 95% confidence interval for the slope of the population regression line. Explain how this interval is consistent with the results of Exercise R12.2.
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?(a) For each value of x, the population of
Inference about the slope b of a least-squares regression line is based on which of the following distributions?(a) The t distribution with n − 1 degrees of freedom(b) The standard Normal
The correlation between total winnings and average number of putts per hole for these players is(a) −0.285. (c) −0.007. (e) 0.285.(b) −0.081. (d) 0.081.
Suppose that the researchers test the hypotheses H0 : b = 0, Ha : b < 0. The value of the t statistic for this test is(a) 2.61. (c) 0.081. (e) −20.24.(b) 2.44. (d) −2.44.The P-value for the test
A 95% confidence interval for the slope b of the population regression line is(a) 7,897,179 ± 3,023,782.(b) 7,897,179 ± 6,047,564.(c) −4,139,198 ± 1,698,371.(d) −4,139,198 ± 3,328,807.(e)
Which of the following would provide evidence that a power law model of the form y = axb, where b ≠ 0 and b ≠ 1, describes the relationship between a response variable y and an explanatory
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
Growth hormones are often used to increase the weight gain of chickens. In an experiment using 15 chickens, 3 chickens were randomly assigned to each of 5 different doses of growth hormone (0, 0.2,
A major agricultural company is testing a new variety of wheat to determine whether it is more resistant to certain insects than is the current wheat variety. The proportion of a current wheat crop
If P(A) = 0.24 and P(B) = 0.52 and events A and B are independent, what is P(A or B)?(a) 0.1248 (b) 0.28(c) 0.6352 (d) 0.76(e) The answer cannot be determined from the given information.
As part of a bear population study, data were gathered on a sample of black bears in the western United States to examine the relationship between the bear’s neck girth (distance around the neck)
The school board in a certain school district obtained a random sample of 200 residents and asked if they were in favor of raising property taxes to fund the hiring of more statistics teachers. The
After a name-brand drug has been sold for several years, the Food and Drug Administration (FDA) will allow other companies to produce a generic equivalent.The FDA will permit the generic drug to be
Which of the following sampling plans for estimating the proportion of all adults in a medium-sized town who favor a tax increase to support the local school system does not suffer from undercoverage
Which of the following is a categorical variable?(a) The weight of automobiles(b) The time required to complete the Olympic marathon(c) The average gas mileage of a hybrid car(d) The brand of shampoo
A large machine is filled with thousands of small pieces of candy, 40% of which are orange. When money is deposited, the machine dispenses 60 randomly selected pieces of candy. The machine will be
A random sample of 900 students at a very large university was asked which social-networking site they used most often during a typical week. Their responses are shown in the table below.Networking
Insurance adjusters are always vigilant about being overcharged for accident repairs. The adjusters suspect that Repair Shop 1 quotes higher estimates than Repair Shop 2. To check their suspicion,
A survey firm wants to ask a random sample of adults in Ohio if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let p^ denote the
A set of 10 cards consists of 5 red cards and 5 black cards. The cards are shuffled thoroughly, and you choose one at random, observe its color, and replace it in the set. The cards are thoroughly
A study of road rage asked random samples of 596 men and 523 women about their behavior while driving. Based on their answers, each respondent was assigned a road rage score on a scale of 0 to 20.
Do hummingbirds prefer store-bought food made from concentrate or a simple mixture of sugar and water? To find out, a researcher obtains 10 identical hummingbird feeders and fills 5, chosen at
A Harris Poll found that 54% of American adults don’t think that human beings developed from earlier species. The poll’s margin of error for 95%confidence was 3%. This means that(a) there is a
Two six-sided dice are rolled and the sum of the faces showing is recorded after each roll. Let X = the number of rolls required until a sum greater than 7 is obtained. If 100 trials are conducted,
Women who are severely overweight suffer economic consequences, a study has shown. They have household incomes that are an average of$6710 lower. The findings are from an eight-year observational
The cell that contributes most to the chi-square statistic is(a) men who developed a rash.(b) men who did not develop a rash.(c) women who developed a rash.(d) women who did not develop a rash.(e)
From the chi-square test performed in this study, we may conclude that(a) there is convincing evidence of an association between the gender of an individual participating in the event and development
Random assignment is part of a well-designed comparative experiment because(a) it is more fair to the subjects.(b) it helps create roughly equivalent groups before treatments are imposed on the
The following back-to-back stemplots compare the ages of players from two minor-league hockey teams (1 | 7 = 17 years).Team A Team B 98777 1 788889 44333221 2 00123444 7766555 2 556679 521 3 023 86 3
A distribution that represents the number of cars X parked in a randomly selected residential driveway on any night is given by xi : 0 1 2 3 4 pi : 0.1 0.2 0.35 0.25 0.15 Which of the following
Which sampling method was used in each of the following settings, in order from I to IV?I. A student chooses for a survey the first 20 students to arrive at school.II. The name of each student in a
Western lowland gorillas, whose main habitat is the central African continent, have a mean weight of 275 pounds with a standard deviation of 40 pounds. Capuchin monkeys, whose main habitat is Brazil
Suppose that the mean weight of a certain type of pig is 280 pounds with a standard deviation of 80 pounds. The weight distribution of pigs tends to be somewhat skewed to the right. A random sample
Which of the following statements about the t distribution with degrees of freedom df is (are) true?I. It is symmetric.II. It has more variability than the t distribution with df + 1 degrees of
A company has been running television commercials for a new children’s product on five different family programs during the evening hours in a large city over a one-month period. A random sample of
Which of the following represents a 95% confidence interval for the true slope of the leastsquares regression line relating the weight of a bear and its neck girth?(a) 20.230 ± 1.695 (d) 20.230 ±
A bear was recently captured whose neck girth was 35 inches and whose weight was 466.35 pounds.If this bear were added to the data set given above, what would be the effect on the value of s?(a) It
An experimenter wishes to test whether or not two types of fish food (a standard fish food and a new product) work equally well at producing fish of equal weight after a two-month feeding program.
A city wants to conduct a poll of taxpayers to determine the level of support for constructing a new city-owned baseball stadium. Which of the following is the primary reason for using a large sample
A standard deck of playing cards contains 52 cards, of which 4 are aces and 13 are hearts. You are offered a choice of the following two wagers:I. Draw one card at random from the deck. You win $10
A distribution of exam scores has mean 60 and standard deviation 18. If each score is doubled, and then 5 is subtracted from that result, what will be the mean and standard deviation, respectively,
In a clinical trial, 30 patients with a certain blood disease are randomly assigned to two groups. One group is then randomly assigned the currently marketed medicine, and the other group receives
A manufacturer of electronic components is testing the durability of a newly designed integrated circuit to determine whether its life span is longer than that of the earlier model, which has a mean
Which of the following statements is supported by these plots?(a) There is no striking evidence that the assumptions for regression inference are violated.(b) The abundance of outliers and
George’s initial fear rating was 0.2 higher than Jonny’s. What does the model predict about their final fear ratings?(a) George’s will be about 0.96 higher than Jonny’s.(b) George’s will be
The table below provides data on the political affiliation and opinion about the death penalty of 850 randomly selected voters from a congressional district.Favor Oppose Total Republican 299 98 397
The body’s natural electrical field helps wounds heal. If diabetes changes this field, it might explain why people with diabetes heal more slowly. A study of this idea compared randomly selected
Can physical activity in youth lead to mental sharpness in old age? A 2010 study investigating this question involved 9344 randomly selected, mostly white women over age 65 from four U.S.states.
In a recent poll, randomly selected New York State residents at various fast-food restaurants were asked if they supported or opposed a “fat tax” on nondiet sugared soda. Thirty-one percent said
Each morning, coffee is brewed in the school workroom by one of three faculty members, depending on who arrives first at work. Mr. Worcester arrives first 10% of the time, Dr. Currier arrives first
Determine the point estimate and margin of error from a confidence interval.
Interpret a confidence interval in context.
Interpret a confidence level in context.
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