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business statistics in practice
The Practice Of Statistics 5th Edition Daren S. Starnes, Josh Tabor - Solutions
A 90% confidence interval for the mean m of a population is computed from a random sample and is found to be 9 ± 3. Which of the following could be the 95% confidence interval based on the same data?(a) 9 ± 2 (b) 9 ± 3 (c) 9 ± 4 (d) 9 ± 8 (e) Without knowing the sample size, any of the above
Suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their first year at a major university. The interval is to have a margin of error of $2. Based on last year’s book sales, we estimate that the standard deviation of the amount spent will be close to
A telephone poll of an SRS of 1234 adults found that 62% are generally satisfied with their lives. The announced margin of error for the poll was 3%. Does the margin of error account for the fact that some adults do not have telephones?(a) Yes. The margin of error includes all sources of error in
A Census Bureau report on the income of Americans says that with 90% confidence the median income of all U.S. households in a recent year was $57,005 with a margin of error of ±$742. This means that (a) 90% of all households had incomes in the range $57,005 ± $742.(b) we can be sure that the
The U.S. Forest Service is considering additional restrictions on the number of vehicles allowed to enter Yellowstone National Park. To assess public reaction, the service asks a random sample of 150 visitors if they favor the proposal. Of these, 89 say “Yes.”(a) Construct and interpret a 99%
How many people live in South African households?To find out, we collected data from an SRS of 48 out of the over 700,000 South African students who took part in the CensusAtSchool survey project.The mean number of people living in a household was 6.208; the standard deviation was 2.576.(a) Is the
A milk processor monitors the number of bacteria per milliliter in raw milk received at the factory. A random sample of 10 one-milliliter specimens of milk supplied by one producer gives the following data:5370 4890 5100 4500 5260 5150 4900 4760 4700 4870 Construct and interpret a 90% confidence
Do Dogs Resemble Their Owners?
State appropriate hypotheses and compute expected counts for a chi-square test for goodness of fit.
Calculate the chi-square statistic, degrees of freedom, and P-value for a chi-square test for goodness of fit.
Perform a chi-square test for goodness of fit.
Conduct a follow-up analysis when the results of a chi-square test are statistically significant.
Aw, nuts! 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 quality-control inspector takes a random sample of 150 nuts from the latest batch.The one-way table below displays the sample data.Nut:
Roulette 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 one-way table below displays the
Aw, nuts! Calculate the chi-square statistic for the data in Exercise 1. Show your work.
Roulette Calculate the chi-square statistic for the data in Exercise 2. Show your work.
Aw, nuts! Refer to Exercises 1 and 3.(a) Confirm that the expected counts are large enough to use a chi-square distribution to calculate the P-value. What degrees of freedom should you use?(b) Sketch a graph like Figure 11.4 (page 685) that shows the P-value.(c) Use Table C to find the P-value.
Roulette Refer to Exercises 2 and 4.(a) Confirm that the expected counts are large enough to use a chi-square distribution to calculate the P-value. What degrees of freedom should you use?(b) Sketch a graph like Figure 11.4 (page 685) that shows the P-value.(c) Use Table C to find the P-value. Then
Birds in the trees Researchers studied the behavior of birds that were searching for seeds and insects in an Oregon forest. In this forest, 54% of the trees were Douglas firs, 40% were ponderosa pines, and 6%were other types of trees. At a randomly selected time during the day, the researchers
Seagulls by the seashore 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
No chi-square 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
No chi-square The principal in Exercise 9 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:School day: Monday Tuesday Wednesday Thursday Friday No. who did homework:34 29 32 28 19
Benford’s law Faked numbers in tax returns, invoices, or expense account claims often display patterns that aren’t present in legitimate records.Some patterns are obvious and easily avoided by a clever crook. Others are more subtle. It is a striking fact that the first digits of numbers in
Housing According to the Census Bureau, the distribution by ethnic background of the New York City population in a recent year was Hispanic: 28% Black: 24% White: 35%Asian: 12% Others: 1%The manager of a large housing complex in the city wonders whether the distribution by race of the complex’s
Skittles 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, lime, orange, strawberry and grape. They were chosen
Is your random number generator working? 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
What’s your sign? 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
Munching Froot Loops Kellogg’s Froot Loops cereal comes in six fruit flavors: orange, lemon, cherry, raspberry, blueberry, and lime. Charise poured out her morning bowl of cereal and methodically counted the number of cereal pieces of each flavor.Here are her data:Flavor: Orange Lemon Cherry
Mendel and the peas 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
You say tomato 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
An appropriate null hypothesis to test whether the food choices are equally popular is(a) H0 :m = 25, where m = 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 Asian food.(c) H0 :nA = nM = nP = nH= 25, where nA is the
The chi-square statistic is(a)(18 − 25)2 25+(22 − 25)2 25+(39 − 25)2 25+(21 − 25)2 25(b)(25 − 18)2 18+(25 − 22)2 22+(25 − 39)2 39+(25 − 21)2 21(c)(18 − 25)25+(22 − 25)25+(39 − 25)25+(21 − 25)25(d)(18 − 25)2 100+(22 − 25)2 100+(39 − 25)2 100+(21 − 25)2 100(e)(0.18 −
The P-value for a chi-square test for goodness of fit is 0.0129. Which of the following is the most appropriate conclusion?(a) Because 0.0129 is less than a = 0.05, reject H0.There is convincing evidence that the food choices are equally popular.(b) Because 0.0129 is less than a = 0.05, reject
Which of the following is false?(a) A chi-square distribution with k degrees of freedom is more right-skewed 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 is determined by the
Reading and grades (1.3) Write a few sentences comparing the distributions of English grades for light and heavy readers.
Reading and grades (10.2) Summary statistics for the two groups from Minitab are provided below.Type of reader N Mean StDev SE Mean Heavy 47 3.640 0.324 0.047 Light 32 3.356 0.380 0.067(a) Explain why it is acceptable to use two-sample t procedures in this setting.(b) Construct and interpret a 95%
Reading and grades (3.2) The Fathom scatterplot below shows the number of books read and the English grade for all 79 students in the study. A leastsquares regression line has been added to the graph.(a) Interpret the meaning of the slope and y intercept in context.(b) The student who reported
Yahtzee (5.3, 6.3) In the game of Yahtzee, 5 sixsided dice are rolled simultaneously. To get a Yahtzee, the player must get the same number on all 5 dice.(a) Luis says that the probability of getting a Yahtzee in one roll of the dice is a 16 b5. Explain why Luis is wrong.(b) Nassir decides to keep
Compare conditional distributions for data in a two-way table.
State appropriate hypotheses and compute expected counts for a chi-square test based on data in a two-way table.
Calculate the chi-square statistic, degrees of freedom, and P-value for a chi-square test based on data in a two-way table.
Perform a chi-square test for homogeneity.
Perform a chi-square test for independence.
Choose the appropriate chi-square test.
Does Background Music Influence What Customers Buy?
Why men and women play sports Do men and women participate in sports for the same reasons?One goal for sports participants is social comparison—the desire to win or to do better than other people.Another is mastery—the desire to improve one’s skills or to try one’s best. A study on why
How are schools doing? The nonprofit group Public Agenda conducted telephone interviews with three randomly selected groups of parents of high school children. There were 202 black parents, 202 Hispanic parents, and 201 white parents. One question asked was “Are the high schools in your state
Why women and men play sports Refer to Exercise 27. Do the data provide convincing evidence of a difference in the distributions of sports goals for male and female undergraduates at the university?(a) State appropriate null and alternative hypotheses for a significance test to help answer this
How are schools doing? Refer to Exercise 28. Do the data provide convincing evidence of a difference in the distributions of opinions about how high schools are doing among black, Hispanic, and white parents?(a) State appropriate null and alternative hypotheses for a significance test to help
Why women and men play sports Refer to Exercises 27 and 29.(a) Check that the conditions for performing the chi-square test are met.(b) Use Table C to find the P-value. Then use your calculator’s c2cdf command.(c) Interpret the P-value from the calculator in context.(d) What conclusion would you
How are schools doing? Refer to Exercises 28 and 30.(a) Check that the conditions for performing the chi-square test are met.(b) Use Table C to find the P-value. Then use your calculator’s c2cdf command.(c) Interpret the P-value from the calculator in context.(d) What conclusion would you draw?
Python eggs How is the hatching of water python eggs influenced by the temperature of the snake’s nest? Researchers randomly assigned newly laid eggs to one of three water temperatures: hot, neutral, or cold. Hot duplicates the extra warmth provided by the mother python, and cold duplicates the
Don’t do drugs! Cocaine addicts need cocaine to feel any pleasure, so perhaps giving them an antidepressant drug will help. A three-year study with 72 chronic cocaine users compared an antidepressant drug called desipramine with lithium (a standard drug to treat cocaine addiction) and a
Sorry, no chi-square How do U.S. residents who travel overseas for leisure differ from those who travel for business? The following is the breakdown by occupation:17 Occupation Leisure travelers (%)Business travelers (%)Professional/technical 36 39 Manager/executive 23 48 Retired 14 3 Student 7 3
Going Nuts The UR Nuts Company sells Deluxe and Premium nut mixes, both of which contain only cashews, brazil nuts, almonds, and peanuts. The Premium nuts are much more expensive than the Deluxe nuts. A consumer group suspects that the two nut mixes are really the same. To find out, the group took
How to quit smoking It’s hard for smokers to quit.Perhaps prescribing a drug to fight depression will work as well as the usual nicotine patch. Perhaps combining the patch and the drug will work better than either treatment alone. Here are data from a randomized, double-blind trial that compared
Preventing strokes Aspirin prevents blood from clotting and so helps prevent strokes. The Second European Stroke Prevention Study asked whether adding another anticlotting drug named dipyridamole would be more effective for patients who had already had a stroke. Here are the data on strokes during
How to quit smoking Perform a follow-up analysis of the test in Exercise 37 by finding the individual components of the chi-square statistic. Which cell(s) contributed most to the final result and in what direction?
Preventing strokes Perform a follow-up analysis of the test in Exercise 38 by finding the individual components of the chi-square statistic. Which cell(s) contributed most to the final result and in what direction?
Attitudes toward recycled products Some people believe recycled products are lower in quality than other products, a fact that makes recycling less practical.Here are data on attitudes toward coffee filters made of recycled paper from a random sample of adults:21 Recycled coffee filter status
Is astrology scientific? The General Social Survey asked a random sample of adults their opinion about whether astrology is very scientific, sort of scientific, or not at all scientific. Here is a two-way table of counts for people in the sample who had three levels of higher education:22 Degree
Attitudes toward recycled products Refer to Exercise 41.(a) State appropriate hypotheses for performing a chisquare test of independence in this setting.(b) Compute the expected counts assuming that H0 is true. Show your work.(c) Calculate the chi-square statistic, df, and P-value.(d) What
Is astrology scientific? Refer to Exercise 42.(a) State appropriate hypotheses for performing a chisquare test of independence in this setting.(b) Compute the expected counts assuming that H0 is true. Show your work.(c) Calculate the chi-square statistic, df, and P-value.(d) What conclusion would
Regulating guns The National Gun Policy Survey asked a random sample of adults, “Do you think there should be a law that would ban possession of handguns except for the police and other authorized persons?” Here are the responses, broken down by the respondent’s level of education:23
Market research Before bringing a new product to market, firms carry out extensive studies to learn how consumers react to the product and how best to advertise its advantages. Here are data from a study of a new laundry detergent.24 The participants are a random sample of people who don’t
Where do young adults live? A survey by the National Institutes of Health asked a random sample of young adults (aged 19 to 25 years), “Where do you live now? That is, where do you stay most often?” Here is the full two-way table (omitting a few who refused to answer and one who claimed to be
Students and catalog shopping What is the most important reason that students buy from catalogs?The answer may differ for different groups of students.Here are results for separate random samples of American and Asian students at a large midwestern university:26 American Asian Save time 29 10 Easy
Treating ulcers Gastric freezing was once a recommended treatment for ulcers in the upper intestine. Use of gastric freezing stopped after experiments showed it had no effect. One randomized comparative experiment found that 28 of the 82 gastric-freezing patients improved, while 30 of the 78
Opinions about the death penalty The General Social Survey asked separate random samples of people with only a high school degree and people with a bachelor’s degree, “Do you favor or oppose the death penalty for persons convicted of murder?”The following table gives the responses of people
Which of the following would be the most appropriate type of graph for these data?(a) A bar chart showing the marginal distribution of opinion about marriage(b) A bar chart showing the marginal distribution of gender(c) A bar chart showing the conditional distribution of gender for each opinion
The appropriate null hypothesis for performing a chi-square test is that(a) equal proportions of female and male teenagers are almost certain they will be married in 10 years.(b) there is no difference between the distributions of female and male teenagers’ opinions about marriage in this
The expected count of females who respond “almost certain” is(a) 487.7. (c) 965. (e) 1174.(b) 525. (d) 1038.8.
The degrees of freedom for the chi-square test for this two-way table are(a) 4. (c) 10. (e) 4876.(b) 8. (d) 20.
For these data, c2 = 69.8 with a P-value of approximately 0. Assuming that the researchers used a significance level of 0.05, which of the following is true?(a) A Type I error is possible.(b) A Type II error is possible.(c) Both a Type I and a Type II error are possible.(d) There is no chance of
When analyzing survey results from a two-way table, the main distinction between a test for independence and a test for homogeneity is(a) how the degrees of freedom are calculated.(b) how the expected counts are calculated.(c) the number of samples obtained.(d) the number of rows in the two-way
Inference recap (8.1 to 11.2) In each of the following settings, state which inference procedure from Chapter 8, 9, 10, or 11 you would use. Be specific.For example, you might say “two-sample z test for the difference between two proportions.” You do not need to carry out any procedures.29(a)
Inference recap (8.1 to 11.2) In each of the following settings, state which inference procedure from Chapter 8, 9, 10, or 11 you would use. Be specific.For example, you might say “two-sample z test for the difference between two proportions.” You do not need to carry out any procedures.30(a)
Design and analysis (4.2)(a) Was this an observational study or an experiment?Justify your answer.(b) Explain why it would not be appropriate to perform a chi-square test in this setting.
Average ratings (1.3, 10.2) The students decided to compare the average ratings of the cafeteria food on the two scales.(a) Find the mean and standard deviation of the ratings for the students who were given the 1-to-5 scale.(b) For the students who were given the 0-to-4 scale, the ratings have a
esting a genetic model Biologists wish to cross pairs of tobacco plants having genetic makeup Gg, indicating that each plant has one dominant gene(G) and one recessive gene (g) for color. Each offspring plant will receive one gene for color from each parent. The Punnett square below shows the
orry, no chi-square We would prefer to learn from teachers who know their subject. Perhaps even preschool children are affected by how knowledgeable they think teachers are. Assign 48 three- and four-year-olds at random to be taught the name of a new toy by either an adult who claims to know about
S tress and heart attacks You read a newspaper article that describes a study of whether stress management can help reduce heart attacks. The 107 subjects all had reduced blood flow to the heart and so were at risk of a heart attack. They were assigned at random to three groups. The article goes on
Sexy magazine ads? Researchers looked at 1509 full-page ads that show a model. The two-way table below shows the main audience of the magazines in which the ads were found (young men, young women, or young adults in general) and whether or not the ad was “sexual.” This was determined based on
Popular kids Who were the popular kids at your elementary school? Did they get good grades or have good looks? Were they good at sports? A study was performed to examine the factors that determine social status for children in grades 4, 5, and 6. Researchers administered a questionnaire to a random
A chi-square test is used to test whether a 0 to 9 spinner is “fair” (that is, the outcomes are all equally likely).The spinner is spun 100 times, and the results are recorded. The degrees of freedom for the test will be(a) 8. (b) 9. (c) 10. (d) 99. (e) None of these
Which hypotheses would be appropriate for performing a chi-square test?(a) The null hypothesis is that the closer students get to graduation, the less likely they are to be opposed to tuition increases. The alternative is that how close students are to graduation makes no difference in their
The conditions for carrying out the chi-square test in exercise T11.2 are I. Independent random samples from the populations of interest.II. All expected counts are at least 5.III. The population sizes are at least 10 times the sample sizes.Which of the conditions is (are) satisfied in this
Assuming H0 is true, the expected number of Hispanic drivers who would receive a ticket is(a) 8. (b) 10.36. (c) 11. (d) 11.84. (e) 12.
We compute the value of the c2 statistic to be 6.58.Assuming that the conditions for inference are met, the P-value of our test is(a) greater than 0.20. (d) between 0.01 and 0.05.(b) between 0.10 and 0.20. (e) less than 0.01.(c) between 0.05 and 0.10.
The category that contributes the largest component to the c2 statistic is(a) White. (c) Hispanic.(b) Black. (d) Other.(e) The answer cannot be determined because this is only a sample.
The appropriate degrees of freedom for the c2 statistic is(a) 1. (b) 2. (c) 3. (d) 4. (e) 5.
The expected count of cases with lymphoma in homes with an HCC is(a)79 # 31 215. (b)10 # 21 215. (c)79 # 31 10. (d)136 # 31 215.(e) None of these.
Which of the following may we conclude, based on the test results?(a) There is convincing evidence of an association between wiring configuration and the chance that a child will develop some form of cancer.(b) HCC either causes cancer directly or is a major contributing factor to the development
A Type I error would occur if we found convincing evidence that(a) HCC wiring caused cancer when it actually didn’t.(b) HCC wiring didn’t cause cancer when it actually did.(c) there is no association between the type of wiring and the form of cancer when there actually is an association.(d)
A large distributor of gasoline claims that 60% of all cars stopping at their service stations choose regular unleaded gas and that premium and supreme are each selected 20% of the time. To investigate this claim, researchers collected data from a random sample of drivers who put gas in their
A study conducted in Charlotte, North Carolina, tested the effectiveness of three police responses to spouse abuse: (1) advise and possibly separate the couple, (2) issue a citation to the offender, and (3) arrest the offender. Police officers were trained to recognize eligible cases. When
In the United States, there is a strong relationship between education and smoking: well-educated people are less likely to smoke. Does a similar relationship hold in France? To find out, researchers recorded the level of education and smoking status of a random sample of 459 French men aged 20 to
Describe the shape, center, and spread of the sampling distribution of p^1− p^2.
Determine whether the conditions are met for doing inference about p1 − p2.
Construct and interpret a confidence interval to compare two proportions.
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