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business statistics in practice

The Practice Of Statistics 5th Edition Daren S. Starnes, Josh Tabor - Solutions

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 = 80.0% R squared (adjusted) = 78.6%s = 0.0204 with 16 − 2 = 14 degrees of freedom Variable Coefficient
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 0.215 Perch 0.008569 0.002456 3.49 0.004 S = 0.1886 R-Sq = 46.5% R-Sq(adj) = 42.7%The model for
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 regression line. Then calculate the confidence interval. Show your work.(c) Interpret the interval
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 the true regression line. Then calculate the confidence interval. Show your work.(c) Interpret the
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, they counted the number of stumps from trees cut by beavers and the number of clusters of beetle
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 least-squares regression analysis on these data is shown below. Construct and interpret a 90% confidence
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 expect the prediction in part (a) to be from the actual number of clusters of beetle larvae? Justify
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 be from the student’s actual height? Justify your answer.
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 the average number of minutes a child spent at the table when lunch was served. “Calories” is the
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 countries for which data were available. The following table displays the data.11 Alcohol from
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 35.72 34.72 34.05 34.13 35.72 Pulse: 152 124 140 152 146 128 Time: 36.17 35.57 35.37 35.57 35.43 36.05
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) price = 127.27 + 1.0466 (appraised value).(d) price = 1.0466 + 127.27 (appraised value).(e) price =
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 appraised value in a population of units when selling price increases by $1000.(c) the average
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 < 0.(c) H0 : b = 0 versus Ha : b ≠ 0.(d) H0 : b > 0 versus Ha : b = 0.(e) H0 : b = 1 versus Ha : b > 1.
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 0.1126.(b) When using this model to predict selling price, the predictions will typically be off 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 scatterplot of x = appraised value and y = selling price did not show a perfect linear
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 block design? Why do you think he chose this experimental design?(c) Explain the purpose of the
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) Use your calculator to find the equation of the leastsquares regression line. Define any symbols you
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 snowmobile?(iii) has never used a snowmobile given that the person belongs to an environmental
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 Yellowstone National Park? Justify your answer.
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 weigh the tree.The biomass is important for studies of ecology, so ecologists commonly estimate it
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 4.0 102 Sheep 6.5 210 Ox 12.0 2030 Horse 16.0 3900(a) Make an appropriate scatterplot for predicting
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 started to fall off the shelf. The top of the ramp was placed at different heights above the floor (that
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 line?(a) A plot of y against x(b) A plot of y against log x(c) A plot of log y against x(d) A plot of
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 that the theoretical relationship between the variables is distance = 490(time)2. A scatterplot of
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 ln(cost)versus Super Bowl number is roughly linear. The least-squares regression line for this association is
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 square root of the y values. Two least-squares regression lines are calculated, one that uses x to
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 0.9 minutes.(a) Find the probability that Marcella’s shower lasts between 3 and 6 minutes on a
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 AP® institute who would say they had tattoos.(b) Does the interval in part (a) provide convincing
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 40 different sessions, the class decided not to use an SRS. Give at least two reasons why you think
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? Define any variables you use.(c) One of the cylinders in the sample had a wall thickness of 0.4 inches.
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 metal?
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 y-values is Normally distributed.(b) The standard deviation s of the population of y-values
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 distribution(c) The chi-square distribution with n − 1 degrees of freedom(d) The t distribution with n −
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 in Question T12.5 is 0.0087. A correct interpretation of this result is that(a) the probability that
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) −4,139,198 ± 3,396,742.
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 variable x?(a) A scatterplot of y versus x looks approximately linear.(b) A scatterplot of ln y versus x
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
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, 0.4, 0.8, and 1.0 milligrams). The subsequent weight gain (in ounces) was recorded for each chicken.
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 lost to insects is 4%. Thus, the company wishes to test the following hypotheses:H0 : p = 0.04 Ha : p
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) and the weight of the bear. A scatterplot of the data reveals a straight-line pattern. The r2-value
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 resulting confidence interval for the true proportion of residents in favor of raising taxes was
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 sold as long as there isn’t convincing evidence that it is less effective than the name brand drug.
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 bias?(a) A random sample of 250 names from the local phone book(b) A random sample of 200 parents
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 purchased by shoppers in a grocery store(e) The average closing price of a particular stock on the
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 recalibrated if a group of 60 candies contains fewer than 18 that are orange.What is the approximate
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 site Male Female Total Facebook 221 283 504 Twitter 42 38 80 LinkedIn 108 87 195 Pinterest 23 26 49
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, the adjusters randomly select 12 cars that were recently involved in an accident and then take each of
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 proportion in the sample who say that they support the increase. Suppose that 40% of all adults in Ohio
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 reshuffled, and you again choose a card at random, observe its color, and replace it in the set. This
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. The respondents were chosen by random digit dialing of telephone numbers.Are the conditions for
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 random, with store-bought food from concentrate and the other 5 with a mixture of sugar and water. The
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 95% chance that the interval (51%, 57%)contains the true percent of American adults who do not think
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, which of the following is most likely to be part of the probability distribution of X?(a) (b)Number
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 study of 10,039 randomly selected women who were 16 to 24 years old when the research began. Does this
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) both (a) and (d).
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 of a rash.(b) mud wrestling causes a rash, especially for women.(c) there is absolutely no evidence
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 subjects.(c) it allows researchers to generalize the results of their experiment to a larger
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 55 Which of the following cannot be justified from the plots?(a) Team A has the same number of
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 statements is correct?(a) This is a legitimate probability distribution because each of the pi-values is
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 school is written on a card, the cards are well mixed, and 10 names are drawn.III. A state agency
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 and a few other parts of Latin America, have a mean weight of 6 pounds with a standard deviation of
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 of 100 pigs is taken. Which of the following statements about the sampling distribution of the 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 freedom.III. As df increases, the t distribution approaches the standard Normal distribution.(a) I only
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 families is taken, and they are asked to indicate which of the five programs they viewed most often
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 ± 20.22(b) 20.230 ± 3.83 (e) 26.7565 ± 3.83(c) 20.230 ± 3.91
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 would decrease the value of s because the added point is an outlier.(b) It would decrease the value
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. The experimenter has two identical fish tanks (1 and 2) to put fish in and is considering how to
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 size in constructing a confidence interval to estimate the proportion of city taxpayers who would
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 if the card drawn is an ace. Otherwise, you lose $1.II. Draw one card at random from the deck. If the
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, of the new scores?(a) mean = 115 and standard deviation = 31(b) mean = 115 and standard deviation =
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 the experimental medicine. Each week, patients report to the clinic where blood tests are
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 life span of 58 months. The company takes a simple random sample of 120 integrated circuits and
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 influential observations in the plots means that the assumptions for regression are clearly violated.(c) These
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 about 0.40 higher than Jonny’s.(c) George’s will be about 0.20 higher than Jonny’s(d)
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 Democrat 77 171 248 Other 118 87 205 Total 494 356 850 Which of the following does not support the
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 normal mice and randomly selected mice bred to spontaneously develop diabetes. The investigators
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. These women were asked about their levels of physical activity during their teenage years, thirties,
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 that they were in favor of such a tax and 66% were opposed. But when asked if they would support
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 50%of the time, and Mr. Legacy arrives first on the remaining mornings. The probability that the
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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