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The Practice Of Statistics For Business And Economics 4th Edition Layth C. Alwan, Bruce A. Craig - Solutions
Which design? The following situations all require inference about a mean or means. Identify each as (1) a single sample, (2) matched pairs, or (3) two independent samples. Explain your answers.(a) You want to estimate the average age of your store’s customers.(b) You do an SRS survey of your
Which design? The following situations all require inference about a mean or means. Identify each as (1) a single sample, (2) matched pairs, or (3) two independent samples. Explain your answers.(a) Your customers are college students. You are interested in comparing the interest in a new product
Study design information. In the previous study, diners were seated alone or in groups of two, three, four, and, in one case, nine (for a total of n 5 16 tables). Also, each table, not each patron, was randomly assigned a particular wine label. Does this information alter how you might perform the
The wine makes the meal? In a recent study, 39 diners were given a free glass of Cabernet Sauvignon to accompany a French meal.35 Although the wine was identical, half the bottle labels claimed the wine was from California, and the other half claimed it was from North Dakota. The following table
Interpreting software output. You use statistical software to perform a significance test of the null hypothesis that two means are equal. The software reports P-values for the two-sided alternative. Your alternative is that the first mean is less than the second mean.(a) The software reports t 5
Number of critical food violations. The results of a major city’s restaurant inspections are available through its online newspaper.34 Critical food violations are those that put patrons at risk of getting sick and must be immediately corrected by the restaurant. An SRS of n 5 300 inspections
t is robust. A manufacturer of flash drives employs a market research firm to estimate retail sales of its products. Here are last month’s sales of 64GB flash drives from an SRS of 50 stores in the Midwest sales region:29 31 45 40 32 21 23 28 19 11 35 21 17 23 22 22 33 31 34 15 32 27 33 24 21 28
LSAT scores. The scores of four classmates on the Law School Admission Test are 166 129 148 153 Find the mean, the standard deviation, and the standard error of the mean. Is it appropriate to calculate a confidence interval based on these data? Explain why or why not.
Design of controls. Apply the sign test to the data in Exercise 7.36 (page 378) to assess whether the subjects can complete a task with a right-hand thread significantly faster than with a left-hand thread. CNTROLS(a) State the hypotheses two ways, in terms of a population median and in terms of
improves Spanish listening skills. State the hypotheses, give the P-value using the binomial table(Table C), and report your conclusion.
Learning Spanish. Use the sign test to assess whether the intensive language training of Exercise
Ego strength: power. You want to compare the ego strengths of MBA students who plan to seek work at consulting firms and those who favor manufacturing firms. Based on the data from Exercise 7.63(page 396), you will use 5 0.7 for planning purposes. The pooled two-sample t test with 5 0.01 will
Power, continued. Repeat the power calculation in the previous exercise for 25, 30, 35, and 40 scoops from each plant. Summarize your power study. A graph of the power against sample size will help.7.92 Margins of error. For each of the sample sizes considered in the previous two exercises,
Comparison of packaging plants:power. Exercise 7.55 (page 395) summarizes data on the number of seeds in one-pound scoops from two different packaging plants. Suppose that you are designing a new study for their next improvement effort. Based on information from the company, you want to identify a
A field trial. The tomato experts who carried out the field trial described in Exercise 7.39 (page 378)suspect that the relative lack of significance there is due to low power. They would like to be able to detect a mean difference in yields of 0.3 pound per plant at the 0.05 significance level.
Credit card fees. The bank in Exercise 7.30(page 377) tested a new idea on a sample of 125 customers. Suppose that the bank wanted to be quite certain of detecting a mean increase of 5 $300 in the credit card amount charged, at the 5 0.01 significance level. Perhaps a sample of only n 5 60
Accuracy of a laboratory scale. To assess the accuracy of a laboratory scale, a standard weight known to weigh 10 grams is weighed repeatedly. The scale readings are Normally distributed with unknown mean (this mean is 10 grams if the scale has no bias).The standard deviation of the scale readings
Average hours per week listening to the radio. Refer to the previous exercise. The Student Monitor also reported that the average amount of time listening to the radio was 11.5 hours.(a) Given an estimated standard deviation of 6.2 hours, what sample size is needed so that the expected margin of
More on apartment rental rates. Refer to the previous exercise. Will the 95% confidence interval include approximately 95% of the rents of all unfurnished one-bedroom apartments in this area?Explain why or why not.7.84 Average hours per week on the Internet. The Student Monitor surveys 1200
Apartment rental rates. You hope to rent an unfurnished one-bedroom apartment in Dallas next year. You call a friend who lives there and ask him to give you an estimate of the mean monthly rate. Having taken a statistics course recently, the friend asks about the desired margin of error and
Sign test for the oil-free frying comparison. Exercise 7.10 (page 371)gives data on the taste of hash browns made using a hot-oil fryer and an oil-free fryer. Is there evidence that the medians are different? State the hypotheses, carry out the sign test, and report your conclusion.
Power and the standard deviation. If the true population standard deviation were 25 instead of the 19.59 hypothesized in Example 7.19, would the power increase or decrease? Explain.
Power and m1 2 m2. If you repeat the calculation in Example 7.19 for other values of 1 2 2 that are smaller than 12, would you expect the power to increase or decrease? Explain.
Another power calculation. Verify your answer to the previous exercise by doing the calculation for the alternative 5 99 minutes.
Power for other values of . If you repeat the calculation in Example 7.18 for values of that are smaller than 109, would you expect the power to be higher or lower than 0.2177? Why?
Changes in sample size. Suppose that, in the setting of the previous exercise, you have the resources to contact 40 recent graduates. If all respond, will your margin of error be larger or smaller than $5000? What if only 50% respond?Verify your answers by performing the calculations.
Starting salaries. In a recent survey by the National Association of Colleges and Employers, the average starting salary for computer science majors was reported to be $61,741.32 You are planning to do a survey of starting salaries for recent computer science majors from your university. Using an
The advantage of pooling. Suppose that in the setting of the previous exercise, you are interested in 95% confidence intervals for the difference rather than significance testing. Find the widths of the intervals for the two procedures (assuming or not assuming equal standard deviations). How do
The advantage of pooling. For the analysis of wheat prices in Example 7.13 (pages 385–386), there are only five observations per month. When sample sizes are small, we have very little information to make a judgment about whether the population standard deviations are equal. The potential gain
Pooled equals unpooled? The software outputs in Figure 7.10 (pages 387–388) give the same value for the pooled and unpooled t statistics. Do some simple algebra to show that this is always true when the two sample sizes n1 and n2 are the same. In other cases, the two t statistics usually differ.
Satterthwaite approximation. The degrees of freedom given by the Satterthwaite approximation are always at least as large as the smaller of n1 2 1 and n2 2 1 and never larger than than the sum n1 1 n2 2 2.In Exercise 7.53 (pages 394–395), you were asked to compare the analyses with and without a
Pooled procedures. Refer to the previous two exercises. Reanalyze the data using the pooled procedure.Does the conclusion depend on the choice of method?The standard deviations are quite different for these data, so we do not recommend use of the pooled procedures in this case.
Fitness and ego. Employers sometimes seem to prefer executives who appear physically fit, despite the legal troubles that may result. Employers may also favor certain personality characteristics. Fitness and personality are related. In one study, middle-aged college faculty who had volunteered for
When is 52 weeks not equal to a year? Refer to the previous exercise. The researchers also had 60 marketing students read an announcement about a construction project. The expected duration was either one year or 52 weeks. Each student was then asked to state the earliest and latest completion
When is 30/31 days not equal to a month?Time can be expressed on different levels of scale; days, weeks, months, and years. Can the scale provided influence perception of time? For example, if you placed an order over the phone, would it make a difference if you were told the package would arrive
Active companies versus failed companies. Examples 7.14 and 7.15 (pages 390–391)compare active and failed companies under the special assumption that the two populations of firms have the same standard deviation. In practice, we prefer not to make this assumption, so let’s analyze the data
Not all dust is the same. Not all dust particles that are in the air around us cause problems for our lungs. Some particles are too large and stick to other areas of our body before they can get to our lungs.Others are so small that we can breathe them in and out and they will not deposit in our
Dust exposure at work. Exposure to dust at work can lead to lung disease later in life. One study measured the workplace exposure of tunnel construction workers.29 Part of the study compared 115 drill and blast workers with 220 outdoor concrete workers. Total dust exposure was measured in milligram
Drive-thru customer service. QSRMagazine.com assessed 1855 drive-thru visits at quickservice restaurants.28 One benchmark assessed was customer service. Responses ranged from “Rude (1)’’to “Very Friendly (5).’’ The following table breaks down the responses according to two of the chains
More on counts of seeds. Refer to the previous exercise.(a) When would a one-sided alternative hypothesis be appropriate in this setting? Explain.(b) What alternative hypothesis would we be testing if we halved the P-value from the previous exercise?
Counts of seeds in one-pound scoops. Refer to Exercise 7.23 (pages 375–376). As part of the Six Sigma quality improvement effort, the company wants to compare scoops of seeds from two different packaging plants. An SRS of 50 one-pound scoops of seeds was collected from Plant 1746, and an SRS of
Noise levels in fitness classes, continued. Refer to the previous exercise. In most countries, the workplace noise standard is 85 db (over eight hours).For every 3 dB increase above that, the amount of exposure time is halved. This means that the exposure time for a dB level of 91 is two hours, and
Noise levels in fitness classes. Fitness classes often have very loud music that could affect hearing.One study collected noise levels (decibels) in both high-intensity and low-intensity fitness classes across eight commercial gyms in Sydney, Australia.27(a) Create a histogram or Normal quantile
Sadness and spending. The “misery is not miserly’’ phenomenon refers to a sad person’s spending judgment going haywire. In a recent study, 31 young adults were given $10 and randomly assigned to either a sad or a neutral group. The participants in the sad group watched a video about the
Trustworthiness and eye color. Why do we naturally tend to trust some strangers more than others? One group of researchers decided to study the relationship between eye color and trustworthiness.25 In their experiment, the researchers took photographs of 80 students (20 males with brown eyes, 20
Advertising in sports, continued. Refer to the previous exercise. This study not only allows a comparison of these two fan groups, but also an assessment of each fan group separately. Write a short paragraph summarizing the key results an advertiser should take away from this study.
Advertising in sports. Can there ever be too many commercials during a sporting event? A group of researchers compared the level of acceptance for commercials between NASCAR and NFL fans.24 Each fan was asked a series of 5-point Likert scale questions to evaluate their level of commercial
Determining significance. For each of the following, answer the question and give a short explanation of your reasoning.(a) A significance test for comparing two means gave t 5 21.86 with 11 degrees of freedom. Can you reject the null hypothesis that the ’s are equal versus the two-sided
Understanding concepts. For each of the following, answer the question and give a short explanation of your reasoning.(a) A 95% confidence interval for the difference between two means is reported as s0.3, 0.7d. What can you conclude about the results of a level 5 0.05 significance test of the
What’s wrong? In each of the following situations, explain what is wrong and why.(a) A researcher wants to test H0: x1 5 x2 versus the two-sided alternative Ha: x1 Þ x2.(b) A study recorded the credit card IQ scores of 100 college freshmen. The scores of the 48 males in the study were compared
Wheat prices revisited. Example 7.12 (pages 384–385) gives summary statistics for the price of wheat in January and July. The two sample standard deviations are relatively close, so we may be willing to assume equal population standard deviations. Calculate the pooled t test statistic and its
Using software. Figure 7.10 (pages 387–388) gives the outputs from five software systems for comparing prices received by wheat producers in July and January for small samples of five producers in each month. Some of the software reports both pooled and unpooled analyses. Which outputs give the
Another two-sample t-test. Refer to Exercise 7.41 (page 382).(a) Perform a significance test to see if there is a difference between the two sets of instructions using 5 0.05.(b) Describe how you could use the 95% confidence interval you calculated in Exercise 7.41 to determine if the there is a
How to assemble a new machine, continued. Refer to Exercise 7.40(page 382). Perform a significance test to see if there is a difference between the two sets of instructions using 5 0.05. Make sure to specify the hypotheses, test statistic, and its P-value, and state your conclusion.
Another two-sample t confidence interval. Refer to the previous exercise. Suppose instead your study results were x1 5 110, x2 5 120, s1 5 8, s2 5 12, n1 5 10, and n2 5 10. Find a 95% confidence interval for the average difference using the second approximation for degrees of freedom.Compare this
How to assemble a new machine. You ran a two-sample study to compare two sets of instructions on how to assemble a new machine. You randomly assign each employee to one of the instructions and measure the time (in minutes) it takes to assemble. Assume that x1 5 110, x2 5 120, s1 5 8, s2 5 12, n1 5
A field trial. An agricultural field trial compares the yield of two varieties of tomatoes for commercial use. The researchers divide in half each of eight small plots of land in different locations and plant each tomato variety on one half of each plot. After harvest, they compare the yields in
Confidence Interval? As CEO, you obtain the salaries of all 31 individuals working in your marketing department. You feed these salaries into your statistical software package, and the output produced includes a confidence interval. Is this a valid confidence interval?Explain your answer.
Is the difference important? Give a 90%confidence interval for the mean time advantage of right-hand over left-hand threads in the setting of the previous exercise. Do you think that the time saved would be of practical importance if the task were performed many times—for example, by an
Design of controls. The design of controls and instruments has a large effect on how easily people can use them. A student project investigated this effect by asking 25 right-handed students to turn a knob (with their right hands) that moved an indicator by screw action.There were two identical
Rudeness and its effect on onlookers. Many believe that an uncivil environment has a negative effect on people. A pair of researchers performed a series of experiments to test whether witnessing rudeness and disrespect affects task performance.16 In one study, 34 participants met in small groups
Executives learn Spanish. A company contracts with a language institute to provide instruction in Spanish for its executives who will be posted overseas.The following table gives the pretest and posttest scores on the Modern Language Association’s listening test in Spanish for 20 executives.15
Corn seed prices. The U.S. Department of Agriculture (USDA) uses sample surveys to obtain important economic estimates. One USDA pilot study estimated the amount a farmer will pay per planted acre for corn seed from a sample of 20 farms. The mean price was reported as $97.59 with a standard error
The influence of big shoppers. Eliminate the three largest observations, and redo parts (a), (b), and(c) of the previous exercise. Do these observations have a large influence on the results?
Supermarket shoppers. A marketing consultant observed 40 consecutive shoppers at a supermarket.One variable of interest was how much each shopper spent in the store. Here are the data (in dollars), arranged in increasing order:5.32 8.88 9.26 10.81 12.69 15.23 15.62 17.00 17.35 18.43 19.50 19.54
Credit card fees. A bank wonders whether omitting the annual credit card fee for customers who charge at least $5000 in a year would increase the amount charged on its credit card. The bank makes this offer to an SRS of 125 of its existing credit card customers. It then compares how much these
Plant capacity. A leading company chemically treats its product before packaging. The company monitors the weight of product per hour that each machine treats.An SRS of 90 hours of production data for a particular machine is collected. The measured variable is in pounds.(a) Describe the
Health care costs. The cost of health care is the subject of many studies that use statistical methods.One such study estimated that the average length of service for home health care among people aged 65 and over who use this type of service is 242 days with a standard error of 21.1 days. Assuming
Alcohol content in beer. In February 2013, two California residents filed a class-action lawsuit against Anheuser-Busch, alleging the company was watering down beers to boost profits.12 They argued that because water was being added, the true alcohol content of the beer by volume is less than the
Investigating the Endowment Effect. Consider an ice-cold glass of lemonade on a hot July day.What is the maximum price you’d be willing to pay for it? What is the minimum price at which you’d be willing to sell it? For most people, the maximum buying price will be less than the minimum selling
Significance test for the average number of seeds.Refer to the previous two exercises.(a) Do these data provide evidence that the average number of seeds in a one-pound scoop is greater than 1550? Using a significance level of 5%, state your hypotheses, the P-value, and your conclusion.(b) Do these
How many seeds on average? Refer to the previous exercise.(a) Find the mean, the standard deviation, and the standard error of the mean for this sample.(b) If you were to calculate the margin of error for the average number of seeds at 90% and 95% confidence, which would be smaller? Briefly explain
Counts of seeds in one-pound scoops. A leading agricultural company must maintain strict control over the size, weight, and number of seeds they package for sale to customers. An SRS of 81 one-pound scoops of seeds was collected as part of a Six Sigma quality improvement effort within the company.
Health insurance costs. The Consumer Expenditure Survey provides information on the buying habits of U.S. consumers.10 In the latest report, the average amount a husband and wife spent on health insurance was reported to be $3251 with a standard error of $89.76. Assuming a sample size of n 5 200,
The return-trip effect. We often feel that the return trip from a destination takes less time than the trip to the destination even though the distance traveled is usually identical. To better understand this effect, a group of researchers ran a series of experiments.9 In one experiment, they
Testing the sticker information. Refer to the previous exercise. The vehicle sticker information for this model stated a city average of 30 mpg. Are these mpg values consistent with the vehicle sticker? Perform a significance test using the 0.05 significance level.Be sure to specify the hypotheses,
Fuel economy. Although the Environmental Protection Agency (EPA) establishes the tests to determine the fuel economy of new cars, it often does not perform them. Instead, the test protocols are given to the car companies, and they perform the tests themselves. To keep the industry honest, the EPA
Business bankruptcies in Canada. Business bankruptcies in Canada are monitored by the Office of the Superintendent of Bankruptcy Canada (OSB).7 Included in each report are the assets and liabilities the company declared at the time of the bankruptcy filing.A study is based on a random sample of 75
A final one-sample t test. The one-sample t statistic for testing H0: 5 20 Ha: , 20 based on n 5 120 observations has the value t 5 23.28.(a) What are the degrees of freedom for this statistic?(b) How would you report the P-value based on Table D?(c) If you have software available, find the
Another one-sample t test. The one-sample t statistic for testing H0: 5 60 Ha: Þ 60 from a sample of n 5 25 observations has the value t 5 21.79.(a) What are the degrees of freedom for t?(b) Locate the two critical values t* from Table D that bracket t. What are the right-tail probabilities p
A one-sample t test. The one-sample t statistic for testing H0: 5 10 Ha: . 10 from a sample of n 5 16 observations has the value t 5 2.23.(a) What are the degrees of freedom for this statistic?(b) Give the two critical values t* from Table D that bracket t.(c) What are the right-tail
Finding critical t*-values. What critical value t* from Table D should be used to calculate the margin of error for a confidence interval for the mean of the population in each of the following situations?(a) A 95% confidence interval based on n 5 9 observations.(b) A 90% confidence interval from
Significance test for the average T-bill interest rate? Consider data on the T-bill interest rate presented in Figure 1.29 (page 53). Would you feel comfortable applying the t procedures in this case? Explain your answer.
Significance test for the average time to start a business? Consider the sample of time data presented in Figure 1.30 (page 54). Would you feel comfortable applying the t procedures in this case? Explain your answer.
95% confidence interval for the difference in taste. To a restaurant owner, the real question is how much difference there is in taste. Use the preceding data to give a 95% confidence interval for the mean difference in taste scores between oil-free and hot-oil frying.
Oil-free deep fryer. Researchers at Purdue University are developing an oil-free deep fryer that will produce fried food faster, healthier, and safer than hot oil.4 As part of this development, they ask food experts to compare foods made with hot oil and their oil-free fryer. Consider the following
Using software to perform a significance test. In Example 7.2(page 360), we tested whether the average time per day of a student using a smartphone was different from the UK average. Use software to perform this test and obtain the exact P-value.
Using software to compute a confidence interval. In Example 7.1(page 360), we calculated the 95% confidence interval for the average daily time a student at your institution uses his or her smartphone. Use software to compute this interval, and verify that you obtain the same interval.
Average quarterly return. A stockbroker determines the short-run direction of the market using the average quarterly return of stock mutual funds. He believes the next quarter will be profitable when the average is greater than 1%.He will get complete quarterly return information soon, but right
Significant? A test of a null hypothesis versus a two-sided alternative gives t 5 2.25.(a) The sample size is 13. Is the test result significant at the 5% level? Explain how you obtained your answer.(b) The sample size is 9. Is the test result significant at the 5% level?(c) Sketch the two t
Apartment rents. Refer to Exercise 7.1 (page 360). Do these data give good reason to believe that the average rent for all advertised one-bedroom apartments is greater than $650 per month? Make sure to state the hypotheses, find the t statistic, degrees of freedom, and P-value, and state your
90% versus 95% confidence interval. If you chose 90%, rather than 95%, confidence in the previous exercise, would your margin of error be larger or smaller? Explain your answer.
More on apartment rents. Refer to Exercise 7.1 (page 360). Construct a 95% confidence interval for the mean monthly rent of all advertised one-bedroom apartments.
Changing the sample size. Refer to the previous exercise. Suppose that instead of an SRS of 25, you sampled 16 advertisements.(a) Would you expect the standard error of the mean to be larger or smaller in this case? Explain your answer.(b) State why you can’t be certain that the standard error
One-bedroom rental apartment. A large city newspaper contains several hundred advertisements for one-bedroom apartments. You choose 25 at random and calculate a mean monthly rent of $703 and a standard deviation of $115.(a) What is the standard error of the mean?(b) What are the degrees of freedom
Median statistic. When a distribution is symmetric, the mean and median will equal. So, when sampling from a symmetric population, it would seem that we would be indifferent in using either the sample mean or sample median for estimating the population mean. Let’s explore this question by
Sample mean distribution. Consider the following distribution for a discrete random variable X:k 22 21 0 1 P(X 5 k) 1/4 1/4 1/4 1/4 Imagine a simple experiment of randomly generating a value for X and recording it and then repeating a second time. Recognize that it is possible to get the same
Welfare reform. A study compares two groups of mothers with young children who were on welfare two years ago. One group attended a voluntary training program offered free of charge at a local vocational school and advertised in the local news media. The other group did not choose to attend the
Significant. Another student, when asked why statistical significance appears so often in research reports, says, “Because saying that results are significant tells us that they cannot easily be explained by chance variation alone.” Do you think that this statement is essentially correct?
Significant. When asked to explain the meaning of “statistically significant at the a 5 0.05 level,” a student says, “This means there is only probability 0.05 that the null hypothesis is true.” Is this a correct explanation of statistical significance?Explain your answer.
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