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The Practice Of Statistics For Business And Economics 4th Edition Layth C. Alwan, Bruce A. Craig - Solutions
Power for a similar significance test. Refer to Exercises 8.80 to 8.82. Suppose you were planning a similar study for a different app. Assume that the population proportions are the same as the sample proportion in the Fox News study. The numbers of smartphone users will be the same for the before
Perform the significance test for the Fox News app. Refer to the previous exercise.(a) What is the test statistic?(b) What is the distribution of the test statistic if the null hypothesis is true?(c) Find the P-value.(d) Use a sketch of the Normal distribution to explain the interpretation or the
A significance test for the Fox News app. Refer to the previous exercise.(a) State an appropriate null hypothesis for this setting.(b) Give an alternative hypothesis for this setting.Explain the meaning of the alternative hypothesis in simple terms, and explain why you chose this particular
Effect of the Fox News app. A survey that sampled smartphone users quarterly compared the proportions of smartphone users who visited the Fox News website before and after the introduction of a Fox News app. A report of the survey stated that 17.6%of smartphone users visited the Fox News website
Worker absences and the bottom line. Refer to Exercises 8.76 through 8.78. Suppose that the companies participating in the new studies are the same as the companies in the original study. Would your answers to any of the parts of Exercises 8.77 and 8.78 change? Explain your answer.
Find the power. Refer to the previous exercise.Consider performing a significance test to compare the population proportions for the two studies. Use 5 0.05 and a one-sided alternative.(a) Find the power of the significance test for each of the following population proportions in the new study:(i)
The new worker absence study. Refer to the previous exercise. Suppose you would like to do a new study next year to see if there has been a change in the percent of companies that do not measure how worker absences affect their company’s bottom line. Assume that a new sample of 1234 companies
Worker absences and the bottom line. A survey of 1234 companies found that 36% of them did not measure how worker absences affect their company’s bottom line.19(a) How many of the companies responded that they do measure how worker absences affect their company’s bottom line? Show your work.(b)
Find the power. Refer to the previous exercise.Consider performing a significance test to compare the population proportions for the two studies. Use 5 0.05 and a two-sided alternative.(a) Find the power of the significance test for each of the following population proportions in the new study:
A new Pew study of Internet of Things. Refer to the previous exercise. Suppose Pew would like to do a new study next year to see if expert opinion has changed since the original study was performed.Assume that a new panel of 1606 experts would be asked the same question.(a) Using 95% confidence,
The Internet of Things. The Internet of Things (IoT) refers to connecting computers, phones, and many other types of devices so that they can communicate and interact with each other.17 A Pew Internet study asked a panel of 1,606 experts whether they thought that the IoT would have “widespread
Find the power. Consider testing the null hypothesis that two proportions are equal versus the two-sided alternative with 5 0.05, 80% power, and equal sample sizes in the two groups.(a) For each of the following situations, find the required sample size: (i) p1 5 0.1 and p2 5 0.2, (ii) p1 5 0.2
Effect of the sample size. Refer to the previous exercise. Similar results from a smaller number of students may not have the same statistical significance.Specifically, suppose that 124 of 136 men surveyed were employed and 106 of 122 women surveyed were employed. The sample proportions are
Summer employment of college students. A university financial aid office polled an SRS of undergraduate students to study their summer employment. Not all students were employed the previous summer. Here are the results for men and women:Men Women Employed Not employed 622 58 533 82 Total 680
Natural versus artificial Christmas trees. In the Christmas tree survey introduced in Case 8.2 (page 428), respondents who had a tree during the holiday season were asked whether the tree was natural or artificial. Respondents were also asked if they lived in an urban area or in a rural area. Of
A corporate liability trial. A major court case on liability for contamination of groundwater took place in the town of Woburn, Massachusetts.A town well in Woburn was contaminated by industrial chemicals. During the period that residents drank water from this well, there were 16 birth defects
College student summer employment.Suppose that 83% of college men and 80% of college women were employed last summer. A sample survey interviews SRSs of 300 college men and 300 college women. The two samples are independent.(a) What is the approximate distribution of the proportion p⁄F of women
What’s wrong? For each of the following, explain what is wrong and why.(a) A 95% confidence interval for the difference in two proportions includes errors due to bias.(b) A t statistic is used to test the null hypothesis that p1 5 p2.(c) If two sample counts are equal, then the sample proportions
Significance test details for tipping. Refer to the previous exercise.(a) Find the test statistic.(b) What is the distribution of the test statistic if the null hypothesis is true?(c) Find the P-value.(d) Use a sketch of a Normal distribution to explain the interpretation of the P-value that you
Significance test for tipping. Refer to the previous two exercises.(a) Give a null hypothesis for this setting in terms of the parameters. Explain the meaning of the null hypothesis in simple terms.(b) Give an alternative hypothesis for this setting in terms of the parameters. Explain the meaning
Confidence interval for tipping. Refer to the previous exercise.(a) Find the proportion of tippers for the red-shirted servers and the proportion of tippers for the servers with other colored shirts.(b) Find a 95% confidence interval for the difference in proportions.(c) Write a short paragraph
To tip or not to tip. A study of tipping behaviors examined the relationship between the color of the shirt worn by the server and whether or not the customer left a tip.15 There were 418 male customers in the study; 40 of the 69 who were served by a server wearing a red shirt left a tip. Of the
Find the sample sizes. Consider the setting in Example 8.11. Change p1 to 0.85 and p2 to 0.90. Find the required sample sizes.
What would the margin of error be? Consider the setting in Example 8.10.(a) Compute the margins of error for n1 5 24 and n2 5 24 for each of the following scenarios: p1 5 0.6, p2 5 0.5; p1 5 0.7, p2 5 0.5; and p1 5 0.8, p2 5 0.5.(b) If you think that any of these scenarios is likely to fit your
What about preference for Commercial B? Refer to Exercise 8.53(page 440), where we changed the roles of the two commercials in our analysis.Answer the questions given in the previous exercise for the data altered in this way. Describe the results of the change.
Gender and commercial preference Refer to Exercise 8.52 (page 439), which compared women and men with regard to their preference for one of two commercials.(a) State appropriate null and alternative hypotheses for this setting. Give a justification for your choice.(b) Use the data given in Exercise
Gender and commercial preference. Refer to Exercises 8.52 and 8.53, where you analyzed data about gender and the preference for one of two commercials. The study also asked the same subjects to give a preference for two other commercials, C and D. Suppose that 92 women preferred Commercial C and
Social media and the supply chain using plus four. Refer to the previous exercise and to Example 8.8. Suppose that the sample sizes were smaller but that the proportions remained approximately the same. Specifically, assume that 17 out of 20 small companies used social media and 13 out of 25 large
Social media and the supply chain using plus four. Refer to Example 8.8(page 438), where we computed a 95% confidence interval for the difference in the proportions of small companies and large companies that use audio/visual sharing through social media as part of their supply chain. Redo the
Rules for means and variances. It is quite easy to verify the mean and standard deviation of the difference D.(a) What are the means and standard deviations of the two sample proportions p⁄1 and p⁄2? (Look at the box on page 256 if you need to review this.)(b) Use the addition rule for means of
Effect of the sample sizes. Suppose p1 5 0.3, n1 5 140, p2 5 0.5, and n2 5 120.(a) Find the mean and the standard deviation of the sampling distribution of p⁄1 2p⁄2.(b) The sample sizes here are four times as large as those in the previous exercise, while the population proportions are the
Rules for means and variances. Suppose p1 5 0.3, n1 5 35, p2 5 0.5, and n2 5 30. Find the mean and the standard deviation of the sampling distribution of p⁄1 2p⁄2.
Nonconforming switches. Refer to Exercises 8.22 and 8.23, where you found a confidence interval and performed a significance test for nonconforming switches. Find the sample size needed for testing the null hypothesis that the population proportion is 0.08 versus the one-sided alternative that the
Are the customers dissatisfied? Refer to Exercise 8.44, where you computed the sample size based on the width of a confidence interval. Now we will use the same setting to determine the sample size based on a significance test. You want to test the null hypothesis that the population proportion is
Justify the cost of the survey. A former editor of the student newspaper agrees to underwrite the study in the previous exercise because she believes the results will demonstrate that most students support an increase in fees. She is willing to provide funds for a sample of size 400. Write a short
Increase student fees? You have been asked to survey students at a large college to determine the proportion that favor an increase in student fees to support an expansion of the student newspaper. Each student will be asked whether he or she is in favor of the proposed increase. Using records
Are the customers dissatisfied? A cell phone manufacturer would like to know what proportion of its customers are dissatisfied with the service received from their local distributor. The customer relations department will survey a random sample of customers and compute a 95% confidence interval for
Be an entrepreneur. A student organization wants to start a nightclub for students under the age of 21. To assess support for this proposal, the organization will select an SRS of students and ask each respondent if he or she would patronize this type of establishment. About 70% of the student body
Change the specs. Refer to the previous exercise.For each of the following variations on the design specifications, state whether the required sample size will be larger, smaller, or the same as that found in Exercise 8.41.(a) Use a 90% confidence interval.(b) Change the allowable margin of error
High-income households on a mailing list. Land’s Beginning sells merchandise through the mail. It is considering buying a list of addresses from a magazine.The magazine claims that at least 30% of its subscribers have high incomes (that is, household income in excess of$120,000). Land’s
More on demographics. In the previous exercise, we arbitrarily chose to state the hypotheses in terms of the proportion of rural respondents. We could as easily have used the proportion of urban respondents.(a) Write hypotheses in terms of the proportion of urban residents to examine how well the
Checking the demographics of a sample. Of the 500 households that responded to the Christmas tree marketing survey, 38% were from rural areas (including small towns), and the other 62% were from urban areas (including suburbs). According to the census, 36% of Indiana households are in rural areas,
Instant versus fresh-brewed coffee. A matched pairs experiment compares the taste of instant coffee with fresh-brewed coffee. Each subject tastes two unmarked cups of coffee, one of each type, in random order and states which he or she prefers. Of the 50 subjects who participate in the study, 19
Shipping the orders on time. As part of a quality improvement program, your mail-order company is studying the process of filling customer orders. According to company standards, an order is shipped on time if it is sent within two working days of the time it is received. You select an SRS of 100
Can we use the z test? In each of the following cases, is the sample large enough to permit safe use of the z test? (The population is very large.)(a) n 5 100 and H0: p 5 0.4.(b) n 5 100 and H0: p 5 0.92.(c) n 5 500 and H0: p 5 0.4.(d) n 5 18 and H0: p 5 0.5.
How would the confidence interval change? Refer to Exercise 8.32. Would a 95%confidence interval be wider or narrower than the one that you found in that exercise? Verify your results by computing the interval.
How would the confidence interval change? Refer to Exercise 8.32. Would a 90%confidence interval be wider or narrower than the one that you found in that exercise? Verify your results by computing the interval.
Plans to study abroad. The survey described in the previous exercise also asked about items related to academics. In response to one of these questions, 43%of first-year students reported that they plan to study abroad.(a) Based on the information available, what is the value of the count of
Students doing community service. In a sample of 116,250 first-year college students, the National Survey of Student Engagement reported that 43%participated in community service or volunteer work.12(a) Find the margin of error for 99% confidence.(b) Here are some facts from the report that
“Guitar Hero” and “Rock Band.” Refer to the previous exercise.(a) How would the result that you reported in part (c) of the previous exercise change if only 25% of the respondents said that they did not currently play a musical instrument?(b) Do the same calculations for a case in which the
“Guitar Hero” and “Rock Band.” An electronic survey of 7061 game players of “Guitar Hero” and “Rock Band” reported that 67% of players of these games who do not currently play a musical instrument said that they are likely to begin playing a real musical instrument in the next two
Mathematician tosses coin 10,000 times! The South African mathematician John Kerrich, while a prisoner of war during World War II, tossed a coin 10,000 times and obtained 5067 heads.(a) Is this significant evidence at the 5% level that the probability that Kerrich’s coin comes up heads is not
Country food and Inuits. Country food includes seal, caribou, whale, duck, fish, and berries and is an important part of the diet of the aboriginal people called Inuits, who inhabit Inuit Nunaat, the northern region of what is now called Canada. A survey of Inuits in Inuit Nunaat reported that 3274
Canadian teens pay to download music. A survey of 416 Canadian teens aged 12 to 17 years were asked about downloading music from the Internet.9 Of these, 316 reported that they have used a fee-based website for their downloads.(a) What proportion of the Canadian teens in the sample used a fee-based
How much influence do social media have on purchasing decisions? A Gallup poll asked this question of 18,525 U.S. adults aged 18 and older.8 The response “No influence at all” was given by 62% of the respondents. Find a 99% confidence for the true proportion of U.S. adults who would choose
How many potential customers should you sample? Refer to the previous exercise. If you want the 95% margin of error to be 0.06 or less, what would you choose for a sample size? Explain how you calculated your answer and show your work.
Customer preferences for your new product.A sample of 50 potential customers was asked to use your new product and the product of the leading competitor. After one week, they were asked to indicate which product they preferred. In the sample, 30 potential customers said that they preferred your
Significance test for nonconforming switches.Refer to the previous exercise. In Example 5.5(pages 247–248), we assumed that the proportion of nonconforming switches in the large shipment was 8%.(a) Give the null and alternative hypotheses for performing a significance test in this setting.(b)
Nonconforming switches. In Example 5.5(pages 247–248), we calculated some binomial probabilities for inspection of a batch of switches from a large shipment of switches. Suppose that in an SRS of 150 switches, we have 10 failures.(a) Find the sample proportion.(b) What is the margin of error for
Soft drink consumption in New Zealand. A survey commissioned by the Southern Cross Healthcare Group reported that 16% of New Zealanders consume five or more servings of soft drinks per week. The data were obtained by an online survey of 2006 randomly selected New Zealanders over 15 years of
Smartphones and purchases. A Google research study asked 5013 smartphone users about how they used their phones. In response to a question about purchases, 2657 reported that they purchased an item after using their smartphone to search for information about the item.6(a) What is the sample size n
Draw some pictures. Consider the binomial setting with n 5 60 and p 5 0.6.(a) The sample proportion p⁄will have a distribution that is approximately Normal. Give the mean and the standard deviation of this Normal distribution.(b) Draw a sketch of this Normal distribution. Mark the location of the
What’s wrong? Explain what is wrong with each of the following.(a) If the P-value for a significance test is 0.5, we can conclude that the null hypothesis is equally likely to be true or false.(b) A student project used a confidence interval to describe the results in a final report. The
What’s wrong? Explain what is wrong with each of the following.(a) The large-sample confidence interval for a population proportion is based on a t statistic.(b) A large-sample significance test for an unknown proportion p is p⁄plus or minus its standard error.(c) You can use a significance
Compute the power for a given sample size. Consider the setting in Example 8.7. You have a budget that will allow you to test 100 subjects. Use software to find the power of the test for this value of n.
Compute the sample size for a different alternative. Refer to Example 8.7.Use software to find the sample size needed for a two-sided test of the null hypothesis that p 5 0.5 versus the two-sided alternative with 5 0.05 and 80%power if the alternative is p 5 0.7.
More information is needed. Refer to the previous exercise. Suppose that, after reviewing the results of the previous survey, you proceeded with preliminary development of the product. Now you are at the stage where you need to decide whether or not to make a major investment to produce and market
Is there interest in a new product? One of your employees has suggested that your company develop a new product. You decide to take a random sample of your customers and ask whether or not there is interest in the new product. The response is on a 1 to 5 scale, with 1 indicating “definitely would
Yes or no? In Example 8.4, we performed a significance test to compare your sunblock with your competitor’s. Success was defined as the outcome where your product provided better protection. Now, take the viewpoint of your competitor, and define success as the outcome where your competitor’s
Construct an example. Make up an example where the large-sample method and the plus four method give very different intervals. Do not use a case where either p⁄5 0 or p⁄5 1.
New-product sales. Yesterday, your top salesperson called on 12 customers and obtained orders for your new product from all 12. Suppose that it is reasonable to view these 12 customers as a random sample of all of her customers.(a) Give the plus four estimate of the proportion of her customers who
Use plus four for net jobs. Refer to Example 8.3 (pages 420–421). Compute the plus four 95% confidence interval, and compare this interval with the one given in that example.
Customer growth and retention strategy. Refer to Exercise 8.2 (page 419).(a) Find SE p⁄, the standard error of p⁄.(b) Give the 95% confidence interval for p in the form of estimate plus or minus the margin of error.(c) Give the confidence interval as an interval of percents.Plus four confidence
Community banks. Refer to Exercise 8.1 (page 419).(a) Find SE p⁄, the standard error of p⁄. Explain the meaning of the standard error in simple terms.(b) Give the 95% confidence interval for p in the form of estimate plus or minus the margin of error.(c) Give the confidence interval as an
Coca-Cola and demographics. A Pew survey interviewed 162 CEOs from U.S. companies. The report of the survey quotes Muhtar Kent, Coca-Cola Company chairman and CEO, on the importance of demographics in developing customer strategies. Kent notes that the population of the United States is aging and
Community banks. The American Bankers Association Community Bank Insurance Survey for 2013 had responses from 151 banks. Of these, 80 were Community Banks, defined to be banks with assets of $1 billion or less.3(a) What is the sample size n for this survey?(b) What is the count X? Describe the
Sign test for the endowment effects. Refer to Exercise 7.26 (page 376) and Exercise 7.124. We can also compare the endowment effects of each chocolate bar. Is there evidence that the median difference in endowment effects (Woolloomooloo minus Oaxaca)is greater than 0? Perform a sign test using the
Ego strengths of MBA graduates: power. In Exercise 7.93 (page 410), you found the power for a study designed to compare the “ego strengths’’ of two groups of MBA students. Now you must design a study to compare MBA graduates who reached partner in a large consulting firm with those who joined
Testing job applicants. The one-hole test is used to test the manipulative skill of job applicants.This test requires subjects to grasp a pin, move it to a hole, insert it, and return for another pin. The score on the test is the number of pins inserted in a fixed time interval. One study compared
Investigating the endowment effect, continued.Refer to Exercise 7.26 (page 376). The group of researchers also asked these same 40 students from a graduate marketing course to consider a Vosges Oaxaca gourmet chocolate bar made with dark chocolate and chili pepper. Test the null hypothesis that
Sign test for time using smartphone. Example 7.1 (page 361) gives data on the daily number of minutes eight students at your institution use their smartphones. Is there evidence that the median amount of minutes is less than 120 minutes(2 hours)? State the hypotheses, carry out the sign test, and
Brain training. The assessment of computerized brain-training programs is a rapidly growing area of research. Researchers are now focusing on who this training benefits most, what brain functions are most susceptible to improvement, and which products are most effective. A recent study looked at
Competitive prices? A retailer entered into an exclusive agreement with a supplier who guaranteed to provide all products at competitive prices. The retailer eventually began to purchase supplies from other vendors who offered better prices. The original supplier filed a legal action claiming
Recovery from wrinkles. Of course, the reason for durable press treatment is to reduce wrinkling.“Wrinkle recovery angle’’ measures how well a fabric recovers from wrinkles. Higher is better. Here are data on the wrinkle recovery angle (in degrees) for the same fabric specimens discussed in
Find a confidence interval. Continue your work from the previous exercise. A fabric manufacturer wants to know how large a strength advantage fabrics treated by the Permafresh method have over fabrics treated by the Hylite process. Give a 95% confidence interval for the difference in mean breaking
Durable press and breaking strength. “Durable press’’ cotton fabrics are treated to improve their recovery from wrinkles after washing. Unfortunately, the treatment also reduces the strength of the fabric. A study compared the breaking strength of fabric treated by two commercial durable
The manufacture of dyed clothing fabrics.Different fabrics respond differently when dyed. This matters to clothing manufacturers, who want the color of the fabric to be just right. Fabrics made of cotton and of ramie are dyed with the same “procion blue’’dye applied in the same way. A
Gender-based expectations? A summary of U.S. hurricanes over the last six decades show that feminine-named hurricanes have resulted in significantly more deaths than masculine-named hurricanes.Why is this? One group of researchers propose this is due to gender-based expectations of severity, which
Alcohol content of wine. The alcohol content of wine depends on the grape variety, the way in which the wine is produced from the grapes, the weather, and other influences. Here are data on the percent of alcohol in wine produced from the same grape variety in the same year by 48 winemakers in the
Another personality trait of hotel managers.Continue your study from the previous exercise. The mean BSRI femininity score in the general male population is 5 5.19. (It does seem odd that the mean femininity score is higher than the mean masculinity score, but such is the world of personality
Personalities of hotel managers. Successful hotel managers must have personality characteristics often thought of as feminine (such as “compassionate’’)as well as those often thought of as masculine (such as“forceful’’). The Bem Sex-Role Inventory (BSRI) is a personality test that gives
Transforming the response. Refer to Exercises 7.109 and 7.111. The researchers state that they took the natural log of the willingness to pay variable in order to “normalize the distribution’’ prior to analysis. Thus, their test results are based on log dollar measurements. For the t
More on snobby salespeople. Refer to Exercise 7.109. Researchers also asked a different 180 women to read the same hypothetical shopping experience but now they entered a mass market(e.g., Gap, American Eagle, H&M). Here are those results (in dollars) for the two conditions.Chain n x s
Evaluate the dress study. Refer to Exercise 7.108. Participants in the study viewed a videotape of a woman described as a 28-year-old senior manager for a Chicago advertising firm who had been working for this firm for seven years. The same woman was used for each of the two conditions, but she
Can snobby salespeople boost retail sales? Researchers asked 180 women to read a hypothetical shopping experience where they entered a luxury store (for example, Louis Vuitton, Gucci, Burberry) and ask a salesperson for directions to the items they seek. For half the women, the salesperson was
Does dress affect competence and intelligence ratings? Researchers performed a study to examine whether or not women are perceived as less competent and less intelligent when they dress in a sexy manner versus a business-like manner. Competence was rated from 1 (not at all) to 7 (extremely), and a
Average number of cars in the drive-thru lane. Refer to the previous exercise. A related benchmark measure was the number of cars observed in the drive-thru lane. A summary for the same two chains is shown here.Chain n x s Taco Bell 308 2.11 2.83 McDonald’s 317 3.81 4.56(a) Is there a difference
Average service time. Recall the drive-thru study in Exercise 7.57 (page 395). Another benchmark that was measured was the service time. A summary of the results (in seconds) for two of the chains is shown here.Chain n x s Taco Bell 308 158.03 35.7 McDonald’s 317 189.49 42.8(a) Is there a
Two-sample t test versus matched pairs t test, continued. Refer to the previous exercise. Perhaps an easier way to see the major difference in the two analysis approaches for these data is by computing 95% confidence intervals for the mean difference.(a) Compute the 95% confidence interval using
Two-sample t test versus matched pairs t test. Consider the following data set. The data were actually collected in pairs, and each row represents a pair.Group 1 Group 2 48.86 48.88 50.60 52.63 51.02 52.55 47.99 50.94 54.20 53.02 50.66 50.66 45.91 47.78 48.79 48.44 47.76 48.92 51.13 51.63(a)
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