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mathematics
practice of statistics

The Practice Of Statistics 6th Edition Daren S. Starnes, Josh Tabor - Solutions

Write a few sentences comparing the distributions of average English grade for light and heavy readers.Do students who read more books for pleasure tend to earn higher grades in English? The boxplots show data from a simple random sample of 79 students at a large high school. Students were
Which of the following is false?a. A chi-square distribution with k degrees of freedom is more rightskewed than a chi-square distribution with k+1 degrees of freedom.b. A chi-square distribution never takes negative values.c. The degrees of freedom for a chi-square test are determined by the sample
The P-value for a chi-square test for goodness of fit is 0.0129. Which of the following is the most appropriate conclusion at a significance level of 0.05?a. Because 0.0129 is less than α = 0.05 reject H0. There is convincing evidence that the food choices are equally popular.b. Because 0.0129 is
The chi-square test statistic isa.b.c.d.e.The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the new school year. She wants to know if each type of food will be equally popular so she can start ordering supplies and making other plans. To
An appropriate null hypothesis to test whether the food choices are equally popular isa. H0: μ = 25 where μ = the mean number of students that prefer each type of food.b. H0: p = 0.25 where p = the proportion of all students who prefer ramen.c. H0: nR = nT = nP = nH = 25 where nR is the
When a fair coin is flipped, we all know that the probability the coin lands on heads is 0.50. However, what if a coin is spun? According to the article “Euro Coin Accused of Unfair Flipping” in the New Scientist, two Polish math professors and their students spun a Belgian euro coin 250 times.
Use your calculator’s RandInt function to generate 200 digits from 0 to 9 and store them in a list.a. State appropriate hypotheses for a chi-square test for goodness of fit to determine whether your calculator’s random number generator gives each digit an equal chance of being generated.b.
Statistics teacher Jason Molesky contacted Mars, Inc., to ask about the color distribution for Skittles candies. Here is an excerpt from the response he received: “The original flavor blend for the Skittles Bite Size Candies is lemon, green apple, orange, strawberry and grape. They were chosen as
Gregor Mendel (1822–1884), an Austrian monk, is considered the father of genetics. Mendel studied the inheritance of various traits in pea plants. One such trait is whether the pea is smooth or wrinkled. Mendel predicted a ratio of 3 smooth peas for every 1 wrinkled pea. In one experiment, he
The University of Chicago’s General Social Survey (GSS) is the nation’s most important social science sample survey. For reasons known only to social scientists, the GSS regularly asks a random sample of people their astrological sign. Here are the counts of responses from a recent GSS of 4344
Do seagulls show a preference for where they land? To answer this question, biologists conducted a study in an enclosed outdoor space with a piece of shore whose area was made up of 56% sand, 29% mud, and 15% rocks. The biologists chose 200 seagulls at random. Each seagull was released into the
Researchers studied the behavior of birds that were searching for seeds and insects in an Oregon forest. In this forest, 54% of the trees are Douglas firs, 40% are ponderosa pines, and 6% are other types of trees. At a randomly selected time during the day, the researchers observed 156 red-breasted
The principal in Exercise 7 also asked the random sample of students to record whether they did all of the homework that was assigned on each of the five school days that week. Here are the data:Explain carefully why it would not be appropriate to perform a chisquare test for goodness of fit using
The paper “Linkage Studies of the Tomato” (Transactions of the Canadian Institute, 1931) reported the following data on phenotypes resulting from crossing tall cut-leaf tomatoes with dwarf potato-leaf tomatoes. We wish to investigate whether the following frequencies are consistent with genetic
Biologists wish to mate pairs of fruit flies having genetic makeup RrCc, indicating that each has one dominant gene (R) and one recessive gene (r) for eye color, along with one dominant (C) and one recessive (c) gene for wing type. Each offspring will receive one gene for each of the two traits
Kellogg’s Froot Loops cereal comes in six colors: orange, yellow, purple, red, blue, and green. Charise randomly selected 120 loops and noted the color of each. Here are her data:Do these data provide convincing evidence at the 5% significance level that Kellogg’s Froot Loops do not contain an
A school’s principal wants to know if students spend about the same amount of time on homework each night of the week. She asks a random sample of 50 students to keep track of their homework time for a week. The following table displays the average amount of time (in minutes) students reported
Refer to Exercise 2.a. Confirm that the expected counts are large enough to use a chisquare distribution to calculate the P-value. What degrees of freedom should you use?b. Use Table C to find the P-value. Then use your calculator’s χ2 cdf command.c. What conclusion would you draw about
Refer to Exercise 1.a. Confirm that the expected counts are large enough to use a chisquare distribution to calculate the P-value. What degrees of freedom should you use?b. Use Table C to find the P-value. Then use your calculator’s χ2 cdf command.c. What conclusion would you draw about the
For each of the following, find the P-value using Table C. Then calculate a more precise value using technology.a. χ2 = 4.49, df = 5b. χ2 = 4.49, df = 1Table C Table C Chi-square distribution critical values Tail probability p df .25 .20 .15 .10 .05 .025 .02 .01 .005 .0025 .001 .0005 1
For each of the following, find the P-value using Table C. Then calculate a more precise value using technology.a. χ2 = 19.03, df = 11b. χ2 = 19.03, df = 3Table C Table C Chi-square distribution critical values Tail probability p df .25 .20 .15 .10 .05 .025 .02 .01 .005 .0025 .001 .0005
Casinos are required to verify that their games operate as advertised. American roulette wheels have 38 slots—18 red, 18 black, and 2 green. In one casino, managers record data from a random sample of 200 spins of one of their American roulette wheels. The table displays the results.a. State
A company claims that each batch of its deluxe mixed nuts contains 52% cashews, 27% almonds, 13% macadamia nuts, and 8% Brazil nuts. To test this claim, a qualitycontrol inspector takes a random sample of 150 nuts from the latest batch. The table displays the sample data.a. State appropriate
What we really want to know is whether coached students improve more than uncoached students, on average, and whether any advantage is large enough to be worth paying for. Use the information above to answer these questions:a. How much more do coached students gain, on average, compared to
Let’s first ask if students who are coached increased their scores significantly, on average.a. You could use the information on the Coached line to carry out either a two-sample t test comparing Try 1 with Try 2 or a paired t test using Gain. Which is the correct test? Why?b. Carry out the
a. A city planner wants to determine if there is convincing evidence of a difference in the average number of cars passing through two different intersections. He randomly selects 12 times between 6:00 a.m. and 10:00 p.m., and he and his assistant count the number of cars passing through each
a. Drowning in bathtubs is a major cause of death in children less than 5 years old. A random sample of parents was asked many questions related to bathtub safety. Overall, 85% of the sample said they used baby bathtubs for infants. Estimate the percent of all parents of young children who use baby
The P-value for a test of versus is 0.227. Which of thefollowing is the correct interpretation of this P-value?a. The probability that is 0.227.b. Given that the true mean difference (Variety A – Variety B) in yield for these two varieties of tomato plants is 0, the probability of
A 95% confidence interval for is given bya.b.c.d.e.Researchers suspect that Variety A tomato plants have a different average yield than Variety B tomato plants. To find out, researchers randomly select 10 Variety A and 10 Variety B tomato plants. Then the researchers divide in half each of 10
A study of the impact of caffeine consumption on reaction time was designed to correct for the impact of subjects’ prior sleep deprivation by dividing the 24 subjects into 12 pairs on the basis of the average hours of sleep they had had for the previous 5 nights. That is, the two with the highest
There are two common methods for measuring the concentration of a pollutant in fish tissue. Do the two methods differ, on average? You apply both methods to each fish in a random sample of 18 carp and usea. The paired t test forb. The one-sample z test for p.c. The two-sample t test ford. The
Refer to Exercise 77. The pilot suspects that the Dubai-to- Doha outbound flight typically takes longer. If so, the difference in flight times will be positive on more days than it is negative. What if either flight is equally likely to take longer? Then we can model the outcome on a randomly
Can students throw a baseball farther than a softball? To find out, researchers conducted a study involving 24 randomly selected students from a large high school. After warming up, each student threw a baseball as far as he or she could and threw a softball as far as he she could, in a random
In each of the following settings, decide whether you should use two sample t procedures to perform inference about a difference in means or paired t procedures to perform inference about a mean difference. Explain your choice.a. To test the wear characteristics of two tire brands, A and B, each of
In each of the following settings, decide whether you should use two sample t procedures to perform inference about a difference in means or paired t procedures to perform inference about a mean difference. Explain your choice.a. To compare the average weight gain of pigs fed two different diets,
Refer to Exercise 88.a. Construct and interpret a 90% confidence interval for the true mean difference. If you already defined parameters and checked conditions in Exercise 88, you don’t need to do them again here.b. Explain how the confidence interval provides more information than the test in
Refer to Exercise 87.a. Construct and interpret a 99% confidence interval for the true mean difference. If you already defined the parameter and checked conditions in Exercise 87, you don’t need to do them again here.b. Explain how the confidence interval provides more information than the test
Do people behave differently on Friday the 13th? Researchers collected data on the number of shoppers at a random sample of 45 grocery stores on Friday the 6th and Friday the 13th in the same month. Then they calculated the difference (subtracting in the order 6th minus 13th) in the number of
Does listening to music while studying help or hinder students’ learning? Two statistics students designed an experiment to find out. They selected a random sample of 30 students from their mediumsized high school to participate. Each subject was given 10 minutes to memorize two different lists
Does drying barley seeds in a kiln increase the yield of barley? A famous experiment by William S. Gosset (who discovered the t distributions) investigated this question. Eleven pairs of adjacent plots were marked out in a large field. For each pair, regular barley seeds were planted in one plot
Many people think it’s faster to order at the drive-thru than to order inside at fast-food restaurants. To find out, Patrick and William used a random number generator to select 10 times over a 2-week period to visit a local Dunkin’ Donuts restaurant. At each of these times, one boy ordered an
Refer to Exercise 78. Explain why it is not appropriate to perform a paired t test about the true mean difference in literacy rates in Islamic countries.Exercise 78.Do males have higher literacy rates than females, on average, in Islamic countries? The following table shows the percent of men
Refer to Exercise 77. Explain why it is not appropriate to perform a paired t test about the true mean difference (Outbound − Return) in flight times between Dubai and Doha. See Exercise 94 for an alternative approach to perform a significance test in this setting.Exercise 77.Emirates Airline
A bank wonders if omitting the annual credit card fee for customers who charge at least $2400 in a year will increase the amount charged on its credit cards. The bank makes this offer to an SRS of 200 of its credit card customers. It then compares how much these customers charge this year with the
Do piano lessons improve the spatial-temporal reasoning of preschool children? A study designed to investigate this question measured the spatial-temporal reasoning of a random sample of 34 preschool children before and after 6 months of piano lessons. The difference (After − Before) in the
Refer to Exercise 76. Construct and interpret a 95% confidence interval for the true mean difference (Bottom – Top) in the zinc concentrations of the wells in this region.Exercise 76.Trace metals found in wells affect the taste of drinking water, and high concentrations can pose a health risk.
Refer to Exercise 75. Construct and interpret a 95% confidence interval for the true mean difference (Weight – Groove) in the estimates of tire wear using these two methods in the population of tires.Exercise 75.Researchers were interested in comparing two methods for estimating tire wear. The
Do males have higher literacy rates than females, on average, in Islamic countries? The following table shows the percent of men and women who were literate in 24 largely Muslim nations at the time of this writing.a. Explain why these are paired data.b. A dotplot of the difference (Male – Female)
Emirates Airline offers one outbound flight from Dubai, United Arab Emirates, to Doha, Qatar, and one return flight from Doha to Dubai each day. An experienced Emirates pilot suspects that the Dubai-to Doha outbound flight typically takes longer. To find out, the pilot collects data about these
Trace metals found in wells affect the taste of drinking water, and high concentrations can pose a health risk. Researchers measured the concentration of zinc (in milligrams/liter) near the top and the bottom of 10 randomly selected wells in a large region. The data are provided in the following
Researchers were interested in comparing two methods for estimating tire wear. The first method used the amount of weight lost by a tire. The second method used the amount of wear in the grooves of the tire. A random sample of 16 tires was obtained. Both methods were used to estimate the total
Researchers in Spain interviewed 7725 13-year-olds about their homework habits—how much time they spent per night on homework and whether they got help from their parents or not—and then had them take a test with 24 math questions and 24 science questions. They found that students who spent
Many manufacturing companies use statistical techniques to ensure that the products they make meet standards. One common way to do this is to take a random sample of products at regular intervals throughout the production shift. Assuming that the process is working properly, the mean
Based on the P-value in Exercise 71, which of the following must be true?a. A 90% confidence interval for will contain 0.b. A 95% confidence interval for will contain 0.c. A 99% confidence interval for will contain 0.d. A 99.9% confidence interval for will contain 0.e. It is
a. Assuming that the true mean road rage score is the same for males and females, there is a 0.002 probability of getting a difference in sample means equal to the one observed in this study.b. Assuming that the true mean road rage score is the same for males and females, there is a 0.002
Which of the following describes a Type II error in the context of this study?a. Finding convincing evidence that the true means are different for males and females, when in reality the true means are the sameb. Finding convincing evidence that the true means are different for males and females,
Does sleep deprivation linger for more than a day? Researchers designed a study using 21 volunteer subjects between the ages of 18 and 25. All 21 participants took a computer-based visual discrimination test at the start of the study. Then the subjects were randomly assigned into two groups. The 11
A random sample of 30 words from Jane Austen’s Pride and Prejudice had a mean length of 4.08 letters with a standard deviation of 2.40. A random sample of 30 words from Henry James’s What Maisie Knew had a mean length of 3.85 letters with a standard deviation of 2.26. Which of the
Do external rewards—things like money, praise, fame, and grades promote creativity? Researcher Teresa Amabile suspected that the answer is no, and that internal motivation enhances creativity. To find out, she recruited 47 experienced creative writers who were college students and divided them at
A company that makes hotel toilets claims that its new pressure assisted toilet reduces the average amount of water used by more than 0.5 gallon per flush when compared to its current model. To test this claim, the company randomly selects 30 toilets of each type and measures the amount of water
In a pilot study, a company’s new cholesterol-reducing drug outperforms the currently available drug. If the data provide convincing evidence that the mean cholesterol reduction with the new drug is more than 10 milligrams per deciliter of blood (mg/dl) greater than with the current drug, the
Breast-feeding mothers secrete calcium into their milk. Some of the calcium may come from their bones, so mothers may lose bone mineral. Researchers compared a random sample of 47 breast-feeding women with a random sample of 22 women of similar age who were neither pregnant nor lactating. They
An educator believes that new reading activities in the classroom will help elementary school pupils improve their reading ability. She recruits 44 third-grade students and randomly assigns them into two groups. One group of 21 students does these new activities for an 8 week period. A control
Refer to Exercise 59.a. Construct and interpret a 95% confidence interval for the difference between the true means. If you already defined parameters and checked conditions in Exercise 59, you don’t need to do them again here.b. Explain how the confidence interval provides more information than
Refer to Exercise 60.a. Construct and interpret a 99% confidence interval for the difference between the true means. If you already defined parameters and checked conditions in Exercise 60, you don’t need to do them again here.b. Explain how the confidence interval provides more information than
Researchers equipped random samples of 56 male and 56 female students from a large university with a small device that secretly records sound for a random 30 seconds during each 12.5-minute period over 2 days. Then they counted the number of words spoken by each subject during each recording period
To see if fish oil can help reduce blood pressure, males with high blood pressure were recruited and randomly assigned to different treatments. Seven of the men were assigned to a 4-week diet that included fish oil. Seven other men were assigned to a 4-week diet that included a mixture of oils that
In many parts of the northern United States, two color variants of the Eastern Gray Squirrel— gray and black—are found in the same habitats. A scientist studying squirrels in a large forest wonders if there is a difference in the sizes of the two color variants. He collects random samples of 40
Do birds learn to time their breeding? Blue titmice eat caterpillars. The birds would like lots of caterpillars around when they have young to feed, but they must breed much earlier. Do the birds learn from one year’s experience when to time their breeding next year? Researchers randomly assigned
Refer to Exercise 54.a. Explain why the sample results give some evidence for the alternative hypothesis.b. Calculate the standardized test statistic and P-value.c. What conclusion would you make?Exercise 54.Many students at Matt’s school claim they can think more clearly while listening to their
Refer to Exercise 53.a. Explain why the sample results give some evidence for the alternative hypothesis.b. Calculate the standardized test statistic and P-value.c. What conclusion would you make?Exercise 53.As the Hispanic population in the United States has grown, businesses have tried to
For a statistics class project, Jonathan and Crystal held an ice-cream eating contest. They randomly selected 29 males and 35 females from their large high school to participate. Each student was given a small cup of ice cream and instructed to eat it as fast as possible. Jonathan and Crystal then
Student researchers Adam, Edward, and Kian wondered if music would affect performance for certain tasks. To find out, they had student volunteers sort a shuffled set of 26 playing cards by face value and by color. Nineteen of the 38 volunteers were randomly assigned to listen to music during the
Many students at Matt’s school claim they can think more clearly while listening to their favorite kind of music. Matt believes that music interferes with thinking clearly. To find out which is true, Matt recruits 84 volunteers and randomly assigns them to two groups. The “Music” group
As the Hispanic population in the United States has grown, businesses have tried to understand what Hispanics like. One study interviewed separate random samples of Hispanic and Anglo customers leaving a bank. Customers were classified as Hispanic if they preferred to be interviewed in Spanish or
A researcher wants to see if birds that build larger nests lay larger eggs. She selects two random samples of nests: one of small nests and the other of large nests. Then she weighs one egg (chosen at random if there is more than one egg) from each nest. A 95% confidence interval for the difference
Catherine and Ana wanted to know if student athletes (students on at least one varsity team) have faster reaction times than non-athletes. They took separate random samples of 33 athletes and 30 non-athletes from their school and tested their reaction time using an online reaction test, which
In a study of heart surgery, one issue was the effect of drugs called beta blockers on the pulse rate of patients during surgery. The available subjects were randomly assigned into two groups. One group received a beta blocker; the other group received a placebo. The pulse rate of each patient at a
College financial aid offices expect students to use summer earnings to help pay for college. But how large are these earnings? One large university studied this question by asking a random sample of 1296 students who had summer jobs how much they earned. The financial aid office separated the
Different varieties of the tropical flower Heliconia are fertilized by different species of hummingbirds. Researchers believe that over time, the lengths of the flowers and the forms of the hummingbirds’ beaks have evolved to match each other. Here are data on the lengths in millimeters for
Observational studies suggest that moderate use of alcohol by adults reduces heart attacks and that red wine may have special benefits. One reason may be that red wine contains polyphenols, substances that do good things to cholesterol in the blood and so may reduce the risk of heart attacks. In an
Mary was interested in comparing the mean word length in articles from a medical journal and an airline’s in-flight magazine. She counted the number of letters in the first 400 words of an article in the medical journal and in the first 100 words of an article in the airline magazine. Mary then
How do the numbers of people living in households in the United Kingdom (U.K.) and South Africa compare? To help answer this question, we chose independent random samples of 50 students from each country. Here is a dotplot of the household sizes reported by the students in the survey:Let the
For their final project, a group of AP® Statistics students wanted to compare the texting habits of males and females. They asked a random sample of students from their school to record the number of text messages sent and received over a 2-day period. Here are their data:Let the true mean
How many pairs of shoes do teenagers have? To find out, a group of AP® Statistics students conducted a survey. They selected a random sample of 20 female students and a separate random sample of 20 male students from their school. Then they recorded the number of pairs of shoes that each student
Refer to Exercise 38.a. Find the probability of getting a difference in sample means x¯M−x¯Wthat’s greater than 2 inches.b. Should we be surprised if the sample mean height for the young men is at least 2 inches greater than the sample mean height for the young women? Explain your
Refer to Exercise 37.a. Find the probability of getting a difference in sample means x¯M−x¯B that’s less than 0 mg/dl.b. Should we be surprised if the sample mean cholesterol level for the 14-year-old boys exceeds the sample mean cholesterol level for the men? Explain your answer.Exercise
The heights of young men follow a Normal distribution with mean μM = 69.3 inches and standard deviation σM = 2.8 inches. The heights of youngwomen follow a Normal distribution with mean μW=64.5 inches and standard deviation σW=2.5 inches. Suppose we select independent SRSs
The level of cholesterol in the blood for all men aged 20 to 34 follows a Normal distribution with mean μM =188 milligrams per deciliter (mg/dl) and standard deviation σM = 41 mg/dl. For 14-year-old boys, blood cholesterol levels follow a Normal distribution with mean μB=170
a. Explain what the value of r2 tells you about how well the least squares line fits the data.b. The mean age of the students’ cars in the sample was x¯ = 5 years. Find the mean mileage of the cars in the sample.c. Interpret the value of s.d. Would it be reasonable to use the least-squares line
a. What is the equation of the least-squares regression line? Be sure to define any symbols you use.b. Interpret the slope of the least-squares line.c. One student reported that her 10-year-old car had 110,000 miles on it. Find and interpret the residual for this data point.Thirty randomly selected
In an experiment to learn whether substance M can help restore memory, the brains of 20 rats were treated to damage their memories. First, the rats were trained to run a maze. After a day, 10 rats (determined at random) were given substance M and 7 of them succeeded in the maze. Only 2 of the 10
Which of the following is the correct margin of error for a 99% confidence interval for the difference in the proportion of male and female college students who worked for pay last summer?a.b.c.d.e.A sample survey interviews SRSs of 500 female college students and 550 male college students.
The researchers report that the results were statistically significant at the 1% level. Which of the following is the most appropriate conclusion?a. Because the P-value is less than 1%, fail to reject H0. There is not convincing evidence that the proportion of male college students in the study who
Let pM and pF be the proportions of all college males and females who worked last summer. The hypotheses to be tested area. H0: pM − pF = 0 versus Ha: pM − pF ≠ 0.b. H0: pM − pF = 0 versus Ha: pM − pF > 0.c. H0: pM − pF = 0 versus Ha:
You may have heard that Botox (botulinum toxin type A) is used for cosmetic surgery, but could it have other beneficial uses? A total of 31 patients who suffered chronic low-back pain were randomly assigned to receive 200 units of either Botox or saline solution through 5 injections at 5 different
Does providing additional information affect responses to a survey question? Two statistics students decided to investigate this issue by asking different versions of a question about texting and driving. Fifty mall shoppers were divided into two groups of 25 at random. The first group was asked
A study reported in the medical journal Fertility and Sterility sought to determine whether the ancient Chinese art of acupuncture could help infertile women become pregnant. A total of 160 healthy women who planned to have IVF were recruited for the study. Half of the subjects (80) were randomly
Two hundred women who were about to undergo IVF served as subjects in an experiment. Each subject was randomly assigned to either a treatment group or a control group. Several people (called intercessors) prayed intentionally for the women in the treatment group, although they did not know the
Refer to Exercise 24.a. Construct and interpret a 95% confidence interval for the difference between the true proportions. Assume that the conditions for inference are met.b. Explain how the confidence interval provides more information than the test in Exercise 24.Exercise 24.Which of two widely

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