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mathematics
statistics
Applied Statistics In Business And Economics 4th Edition David Doane, Lori Seward - Solutions
A sample of size n = 19 has variance s2 = 1.96. At α = .05 in a right-tailed test, does this sample contradict the hypothesis that σ2 = 1.21?
pH is a measure of acidity that winemakers must watch. A "healthy wine" should have a pH in the range 3.1 to 3.7. The target standard deviation is σ = 0.10 (i.e., σ2 = 0.01). The pH measurements for a sample of 16 bottles of wine are shown below. At α = .05 in a two-tailed test, is the
In U.S. hospitals, the average length of stay (LOS) for a diagnosis of pneumonia is 137 hours with a standard deviation of 25 hours. The LOS (in hours) for a sample of 12 pneumonia patients at Santa Theresa Memorial Hospital is shown below. In a two-tailed test at α = .05, is this sample
Suppose you always reject the null hypothesis, regardless of any sample evidence.(a) What is the probability of Type II error?(b) Why is this a bad policy?
Suppose the judge decides to acquit all defendants, regardless of the evidence.(a) What is the probability of Type I error?(b) Why is this a bad policy?
High blood pressure, if untreated, can lead to increased risk of stroke and heart attack. A common definition of hypertension is diastolic blood pressure of 90 or more. (a) State the null and alternative hypotheses for a physician who checks your blood pressure. (b) De ne Type I and II error. What
A nuclear power plant replaces its ID card facility access system cards with a biometric security system that scans the iris pattern of the employee and compares it with a data bank. Users are classified as authorized or unauthorized.(a) State the null and alternative hypotheses.(b) De ne Type I
A test-preparation company advertises that its training program raises SAT scores by an average of at least 30 points. A random sample of test-takers who had completed the training showed a mean increase smaller than 30 points.(a) Write the hypotheses for a left-tailed test of the mean.(b) Explain
Pap smears are a test for abnormal cancerous and precancerous cells taken from the cervix. (a) State a pair of hypotheses and then explain the meaning of a false negative and a false positive. (b) Why is the null hypothesis "null"? (c) Who bears the cost of each type of error?
In a commercially available fingerprint scanner (e.g., for your home or office PC), false acceptances are 1 in 25 million, with false rejection rates of 3 percent. (a) De ne Type I and II error. (b) Why do you suppose the false rejection rate is so high compared with the false acceptance rate?
Malcheon Health Clinic claims that the average waiting time for a patient is 20 minutes or less. A random sample of 15 patients shows a mean wait time of 24.77 minutes with a standard deviation of 7.26 minutes.(a) Write the hypotheses for a right-tailed test, using the clinic's claim as the null
The sodium content of a popular sports drink is listed as 220 mg in a 32-oz bottle. Analysis of 10 bottles indicates a sample mean of 228.2 mg with a sample standard deviation of 18.2 mg.(a) Write the hypotheses for a two-tailed test of the claimed sodium content.(b) Calculate the t test statistic
A can of peeled whole tomatoes is supposed to contain an average of 19 ounces of tomatoes (excluding the juice). The actual weight is a normally distributed random variable whose standard deviation is known to be 0.25 ounce. (a) In quality control, would a one-tailed or two-tailed test be used?
At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a mean of 520 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml.(a) Which sampling distribution would you use if random samples of 10 bottles are to be weighed? Why?(b)
On eight Friday quizzes, Bob received scores of 80, 85, 95, 92, 89, 84, 90, 92. He tells Prof. Hardtack that he is really a 90+ performer, but this sample just happened to fall below his true performance level.(a) State an appropriate pair of hypotheses.(b) State the formula for the test statistic
Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10 or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample
A U.S. dime weighs 2.268 grams when minted. A random sample of 15 circulated dimes showed a mean weight of 2.256 grams with a standard deviation of .026 gram.(a) Using α = .05, is the mean weight of all circulated dimes lower than the mint weight? State your hypotheses and decision rule.(b) Why
A coin was flipped 60 times and came up heads 38 times.(a) At the .10 level of significance, is the coin biased toward heads? Show your decision rule and calculations.(b) Calculate a p-value and interpret it.
A sample of 100 one-dollar bills from the Subway cash register revealed that 16 had some- thing written on them besides the normal printing (e.g., "Bob ♥ Mary").(a) At α = .05, is this sample evidence consistent with the hypothesis that 10 percent or fewer of all dollar bills have anything
A sample of 100 mortgages approved during the current year showed that 31 were issued to a single-earner family or individual. The historical percentage is 25 percent.(a) At the .05 level of significance in a right-tailed test, has the percentage of single-earner or individual mortgages risen?
A state weights-and-measures standard requires that no more than 5 percent of bags of Halloween candy be underweight. A random sample of 200 bags showed that 16 were under- weight.(a) At α = .025, is the standard being violated? Use a right-tailed test and show your work.(b) Find the p-value.
Ages for the 2009 Boston Red Sox pitchers are shown below.(a) Assuming this is a random sample of major league pitchers, at the 5 percent level of significance does this sample show that the true mean age of all American League pitchers is over 30 years? State your hypotheses and decision rule and
The EPA is concerned about the quality of drinking water served on airline fights. A sample of 112 fights found unacceptable bacterial contamination on 14 fights.(a) At α = .05, does this sample show that more than 10 percent of all fights have contaminated water?(b) Find the p-value.
A web-based company has a goal of processing 95 percent of its orders on the same day they are received. If 485 out of the next 500 orders are processed on the same day, would this prove that they are exceeding their goal, using α = .025?
In the Big Ten (the NCAA sports league), a sample showed that only 267 out of 584 fresh- men football players graduated within 6 years.(a) At α = .05, does this sample contradict the claim that at least half graduate within 6 years? State your hypotheses and decision rule.(b) Calculate the p-value
An auditor reviewed 25 oral surgery insurance claims from a particular surgical office, deter- mining that the mean out-of-pocket patient billing above the reimbursed amount was $275.66 with a standard deviation of $78.11.(a) At the 5 percent level of significance, does this sample prove a
The average service time at a Noodles & Company restaurant was 3.5 minutes in the previous year. Noodles implemented some time-saving measures and would like to know if they have been effective. They sample 20 service times and find the sample average is 3.2 minutes with a sample standard
A digital camcorder repair service has set a goal not to exceed an average of 5 working days from the time the unit is brought in to the time repairs are completed. A random sample of 12 repair records showed the following repair times (in days): 9, 2, 5, 1, 5, 4, 7, 5, 11, 3, 7, 2. At α = .05, is
A recent study by the Government Accountability Office found that consumers got correct answers about Medicare only 67 percent of the time when they called 1-800-MEDICARE.(a) At α = .05, would a subsequent audit of 50 randomly chosen calls with 40 correct answers suffice to show that the
Beer shelf life is a problem for brewers and distributors because when beer is stored at room temperature, its favor deteriorates. When the average furfuryl ether content reaches 6 g per liter, a typical consumer begins to taste an unpleasant chemical favor. (a) At α = .05, would the following
(a) A statistical study reported that a drug was effective with a p-value of .042. Explain in words what this tells you. (b) How would that compare to a drug that had a p-value of .087?
Bob said, "Why is a small p-value significant, when a large one isn't? That seems backwards." Try to explain it to Bob, giving an example to make your point.
An automaker states that its cars equipped with electronic fuel injection and computerized engine controls will start on the fist try (hot or cold) 99 percent of the time. A survey of 100 new car owners revealed that 3 had not started on the first try during a recent cold snap. (a) At α = .025,
Do a two-sample test for equality of means assuming equal variances. Calculate the p-value.a. Comparison of GPA for randomly chosen college juniors and seniors: 1 = 3.05s s1 = .20, n1 = 15, 2 = 3.25, s2 = 30, n2 = 15, α = .025, left-tailed test.b. Comparison of average commute miles for randomly
A special bumper was installed on selected vehicles in a large fleet. The dollar cost of body repairs was recorded for all vehicles that were involved in accidents over a 1-year period. Those with the special bumper are the test group and the other vehicles are the control group, shown below. Each
In trials of an experimental Internet-based method of learning statistics, pre-tests and post- tests were given to two groups: traditional instruction (22 students) and Internet-based (17 students). Pre-test scores were not significantly different. On the post-test, the first group (traditional
Construct a 95 percent confidence interval for the difference of mean monthly rent paid by undergraduates and graduate students. What do you conclude?
(a) At α = .05, does the following sample show that daughters are taller than their mothers?(b) Is the decision close?(c) Why might daughters tend to be taller than their mothers? Why might they not?
An experimental surgical procedure is being studied as an alternative to the old method. Both methods are considered safe. Five surgeons perform the operation on two patients matched by age, sex, and other relevant factors, with the results shown. The time to complete the surgery (in minutes) is
Blue Box is testing a new "half price on Tuesday" policy on DVD rentals at a sample of 10 locations.(a) At α = .10, do the data show that the mean number of Tuesday rentals has increased?(b) Is the decision close?(c) Are you convinced?
The U.S. government's "Cash for Clunkers" program encouraged individuals to trade in their old gas-guzzlers for new, more efficient vehicles. At α = .05, do the data below sup- port the hypothesis that the gain in mpg was more than 5 mpg? The null hypothesis is H0 : µd ‰¤ 5 mpg.
The coach told the high school swim team that times in the 200-yard individual medley in the Division I-AA Swim Championships typically are more than 1/2 second faster than their seed times going into the meet. At α = .05, do these times (in seconds) for 26 male competitors (actual data with
Below is a random sample of shoe sizes for 12 mothers and their daughters.(a) At α = .01, does this sample show that women's shoe sizes have increased? State your hypotheses and show all steps clearly.(b) Is the decision close?(c) Are you convinced?(d) Why might shoe sizes change over time?
A newly installed automatic gate system was being tested to see if the number of failures in 1,000 entry attempts was the same as the number of failures in 1,000 exit attempts. A random sample of eight delivery trucks was selected for data collection. Do these sample results show that there is a
Repeat the previous exercise, assuming unequal variances. Calculate the p-value using Excel, and show the Excel formula you used.Precious exercisea. Comparison of GPA for randomly chosen college juniors and seniors: 1 = 3.05s s1 = .20, n1 = 15, 2 = 3.25, s2 = 30, n2 = 15, α = .025, left-tailed
Calculate the test statistic and p-value for a test of equal population proportions. What is your conclusion?a. Right-tailed test, α = .10, x1 = 228, n1 = 240, x2 5 703, n2 = 760b. Left-tailed test, α = .05, x1 = 36, n1 = 80, x2 = 66, n2 = 120c. Two-tailed test, α = .05, x1 = 52, n1 = 80, x2 =
Calculate the test statistic and p-value for a test of equal population proportions. What is your conclusion?a. Left-tailed test, α = .10, x1 = 28, n1 = 336, x2 = 14, n2 = 112b. Right-tailed test, α = .05, x1 = 276, n1 = 300, x2 = 440, n2 = 500c. Two-tailed test, α = .10, x1 = 35, n1 = 50, x2 =
Find the sample proportions and test statistic for equal proportions. Find the p-value.a. Dissatisfied workers in two companies: x1 = 40, n1 = 100, x2 = 30, n2 = 100, α = .05, two-tailed test.b. Rooms rented at least a week in advance at two hotels: x1 = 24, n1 = 200, x2 = 12, n2 = 50, α = .01,
Find the test statistic and do the two-sample test for equality of proportions.a. Repeat buyers at two car dealerships: p1 = .30, n1 = 50, p2 = .54, n2 = 50, left-tailed test.b. Honor roll students in two sororities: p1 = .45, n1 = 80, p2 = .25, n2 = 48, two-tailed test.c. First-time Hawaii
During the period 1990–1998 there were 46 Atlantic hurricanes, of which 19 struck the United States. During the period 199922006 there were 70 hurricanes, of which 45 struck the United States.State the hypotheses to test whether the percentage of hurricanes that strike the United States is
In 2006, a sample of 200 in-store shoppers showed that 42 paid by debit card. In 2009, a sample of the same size showed that 62 paid by debit card.(a) Formulate appropriate hypotheses to test whether the percentage of debit card shoppers increased.(b) Carry out the test at α = .01.(c) Find the
A survey of 100 mayonnaise purchasers showed that 65 were loyal to one brand. For 100 bath soap purchasers, only 53 were loyal to one brand. Perform a two-tailed test comparing the proportion of brand-loyal customers at α = .05.
A 20-minute consumer survey mailed to 500 adults aged 25–34 included a $5 Starbucks gift certificate. The same survey was mailed to 500 adults aged 25–34 without the gift certificate. There were 65 responses from the first group and 45 from the second group. Perform a two- tailed test comparing
Is the water on your airline fight safe to drink? It is not feasible to analyze the water on every fight, so sampling is necessary. The Environmental Protection Agency (EPA) found bacterial contamination in water samples from the lavatories and galley water taps on 20 of 158 randomly selected U.S.
When tested for compliance with Sarbanes-Oxley requirements for financial records and fraud protection, 14 of 180 publicly traded business services companies failed, com- pared with 7 of 67 computer hardware, software, and telecommunications companies.(a) Is this a statistically significant
Is there a difference in the average number of years' seniority between returning part-time seasonal employees and returning full-time seasonal employees at a Vail Resorts' ski mountain? From a random sample of 191 returning part-time employees, the average seniority, 1, was 4.9 years with a
In 2009, a sample of 200 in-store shoppers showed that 42 paid by debit card. In 2012, a sample of the same size showed that 62 paid by debit card.(a) Formulate appropriate hypotheses to test whether the percentage of debit card shoppers increased by more than 5 percent, using α = .10.(b) Find the
From a telephone log, an executive finds that 36 of 128 incoming telephone calls last week lasted at least 5 minutes. She vows to make an effort to reduce the length of time spent on calls. The phone log for the next week shows that 14 of 96 incoming calls lasted at least 5 minutes.(a) At α = .05,
A 30-minute consumer survey mailed to 500 adults aged 25234 included a $10 gift certificate to Borders. The same survey was mailed to 500 adults aged 25234 without the gift certificate. There were 185 responses from the first group and 45 from the second group.(a) At α = .025, did the gift
The American Bankers Association reported that, in a sample of 120 consumer purchases in France, 60 were made with cash, compared with 26 in a sample of 50 consumer purchases in the United States. Construct a 90 percent confidence interval for the difference in proportions.
A study showed that 36 of 72 cell phone users with a headset missed their exit, compared with 12 of 72 talking to a passenger. Construct a 95 percent confidence interval for the difference in proportions.
A survey of 100 cigarette smokers showed that 71 were loyal to one brand, compared to 122 of 200 toothpaste users. Construct a 90 percent confidence interval for the difference in proportions.
Which samples show unequal variances? Use α = .10 in all tests. Show the critical values and degrees of freedom clearly and illustrate the decision rule.a. s1 = 10.2, n1 = 22, s2 = 6.4, n2 = 16, two-tailed testb. s1 = 0.89, n1 = 25, s2 = 0.67, n2 = 18, right-tailed testc. s1 = 124, n1 = 12, s2 =
Which samples show unequal variances? Use α = .05 in all tests. Show the critical values and degrees of freedom clearly and illustrate the decision rule.a. s1 = 5.1, n1 5 11, s2 = 3.2, n2 = 8, two-tailed testb. s1 = 221, n1 5 8, s2 = 445, n2 = 8, left-tailed testc. s1 = 67, n1 5 10, s2 = 15, n2 =
Researchers at the Mayo Clinic have studied the effect of sound levels on patient healing and have found a significant association (louder hospital ambient sound level is associated with slower postsurgical healing). Based on the Mayo Clinic's experience, Ardmore Hospital in- stalled a new vinyl
A manufacturing process drills holes in sheet metal that are supposed to be .5000 cm in diameter. Before and after a new drill press is installed, the hole diameter is carefully measured (in cm) for 12 randomly chosen parts. At α = .05, do these independent random samples prove that the new
The average mpg usage for a 2009 Toyota Prius for a sample of 10 tanks of gas was 45.5 with a standard deviation of 1.8. For a 2009 Honda Insight, the average mpg usage for a sample of 10 tanks of gas was 42.0 with a standard deviation of 2.3.(a) Assuming equal variances, at α = .01, is the true
Examine the data below showing the weights (in pounds) of randomly selected checked bags for an airline's fights on the same day.(a) At α = .05, is the mean weight of an international bag greater? Show the hypotheses, decision rule, and test statistic.(b) At α = .05, is the variance greater
The top food snacks consumed by adults aged 1854 are gum, chocolate candy, fresh fruit, potato chips, breath mints/candy, ice cream, nuts, cookies, bars, yogurt, and crackers. Out of a random sample of 25 men, 15 ranked fresh fruit in their top five snack choices. Out of a random sample of 32
In an early home game, an NBA team made 66 of their 94 free throw attempts. In one of their last home games, the team made 68 of 89 attempts.(a) At α = .10, did the team significantly improve its free throw percentage (left-tailed test)?(b) Use Excel to calculate the p-value and interpret it.
Do a larger proportion of college students than young children eat cereal? Researchers surveyed both age groups to find the answer. The results are shown in the table below.(a) State the hypotheses used to answer the question.(b) Using α = .05, state the decision rule and sketch it.(c) Find the
A 2005 study found that 202 women held board seats out of a total of 1,195 seats in the Fortune 100 companies. A 2003 study found that 779 women held board seats out of a total of 5,727 seats in the Fortune 500 companies. Treating these as random samples (board seat assignments change often), can
A study of the Fortune 100 board of director members showed that there were 36 minority women holding board seats out of 202 total female board members. There were 142 minority men holding board seats out of 993 total male board members.(a) Treating the findings from this study as samples,
To test his hypothesis that students who finish an exam first get better grades, a professor kept track of the order in which papers were handed in. Of the first 25 papers, 10 received a B or better compared with 8 of the last 24 papers handed in. Is the first group better, at 5 .10?(a) State your
How many full-page advertisements are found in a magazine? In an October issue of Muscle and Fitness, there were 252 ads, of which 97 were full-page. For the same month, the magazine Glamour had 342 ads, of which 167 were full-page.(a) Is the difference significant at α = .01?(b) Find the
Male and female students in a personal finance class were asked to count how much cash they carried.(a) At α = .01, can you conclude that the males carry more cash on average? Assume Cash unequal population variances.(b) Is it reasonable to assume unequal variances?
After John F. Kennedy Jr. was killed in an airplane crash at night, a survey was taken, asking whether a non instrument-rated pilot should be allowed to y at night. Of 409 New York State residents, 61 said yes. Of 70 aviation experts who were asked the same question, 40 said yes.(a) At α = .01,
When the background music tempo was slow, the mean amount of bar purchases for a sample of 17 restaurant patrons was $30.47 with a standard deviation of $15.10. When the background music tempo was fast, the mean amount of bar purchases for a sample of 14 patrons in the same restaurant was $21.62
A ski company in Vail owns two ski shops, one on the east side and one on the west side. Sales data showed that at the eastern location there were 56 pairs of large gloves sold out of 304 total pairs sold. At the western location there were 145 pairs of large gloves sold out of 562 total pairs
At a University of Colorado woman's home basketball game, a random sample of 25 con- cession purchases showed a mean of $7.12 with a standard deviation of $2.14. For the next week's home game, the admission ticket had a discount coupon for popcorn printed on the back. A random sample of 25
Vail Resorts tracks the proportion of seasonal employees who are rehired each season. Rehiring a seasonal employee is beneficial in many ways, including lowering the costs incurred during the hiring process such as training costs. A random sample of 833 full-time and 386 part-time seasonal
Does a "follow-up reminder" increase the renewal rate on a magazine subscription? A magazine sent out 760 subscription renewal notices (without a reminder) and got 703 renewals. As an experiment, they sent out 240 subscription renewal notices (with a reminder) and got 228 renewals.(a) At α = .05,
A study revealed that the 30-day readmission rate was 31.4 percent for 370 patients who received after-hospital care instructions (e.g., how to take their medications) compared to a readmission rate of 45.1 percent for 368 patients who did not receive such information.(a) Set up the hypotheses to
In a marketing class, 44 student members of virtual (Internet) project teams (group 1) and 42 members of face-to-face project teams (group 2) were asked to respond on a 15 scale to the question: "As compared to other teams, the members helped each other." For group 1 the mean was 2.73 with a
In San Francisco, a sample of 3,106 wireless routers showed that 40.12 percent used encryption (to prevent hackers from intercepting information). In Seattle, a sample of 3,013 wireless routers showed that 25.99 percent used encryption.(a) Set up hypotheses to test whether or not the population
Former U.S. Vice President Dick Cheney received a lot of publicity after his fourth heart attack. A portable defibrillator was surgically implanted in his chest to deliver an electric shock to re- store his heart rhythm whenever another attack was threatening. Researchers at the University of
In 2009 Noodles & Company introduced spaghetti and meatballs to their menu. Before putting it on the menu, they performed taste tests to determine the best-tasting spaghetti sauce. In a paired comparison, 70 tasters were asked to rate their satisfaction with two different - sauces on a scale of
Has the cost to outsource a standard employee background check changed? A random sample of 10 companies in spring 2010 showed a sample average of $105 with a sample standard deviation equal to $32. A random sample of 10 different companies in spring 2012 resulted in a sample average of $75 with a
Are women's feet getting bigger? Retailers in the last 20 years have had to increase their stock of larger sizes. Wal-Mart Stores, Inc., and Payless Shoe Source, Inc., have been aggressive in stocking larger sizes, and Nordstrom's reports that its larger sizes typically sell out first. Assuming
From her firm's computer telephone log, an executive found that the mean length of 64 telephone calls during July was 4.48 minutes with a standard deviation of 5.87 minutes. She vowed to make an effort to reduce the length of calls. The August phone log showed 48 telephone calls whose mean was
An experimental bumper was designed to reduce damage in low-speed collisions. This bumper was installed on an experimental group of vans in a large feet, but not on a control group. At the end of a trial period, accident data showed 12 repair incidents for the experimental group and 9 repair
Based on the sample data below, is the average Medicare spending in the northern region significantly less than the average spending in the southern region at the 1 percent level?(a) State the hypotheses and decision rule.(b) Find the test statistic assuming unequal variances.(c) State your
In a 15-day survey of air pollution in two European capitals, the mean particulate count (micrograms per cubic meter) in Athens was 39.5 with a standard deviation of 3.75, while in London the mean was 31.5 with a standard deviation of 2.25.(a) Assuming equal population variances, does this evidence
One group of accounting students took a distance learning class, while another group took the same course in a traditional classroom. At α = .10, is there a significant difference in the mean scores listed below?(a) State the hypotheses.(b) State the decision rule and sketch it.(c) Find the test
Do male and female school superintendents earn the same pay? Salaries for 20 males and 17 females in a certain metropolitan area are shown below. At α = .01, were the mean superintendent salaries greater for men than for women?(a) State the hypotheses.(b) State the decision rule and sketch
The average take-out order size for Ashoka Curry House restaurant is shown. Assuming equal variances, at α = .05, is there a significant difference in the order sizes?(a) State the hypotheses.(b) State the decision rule and sketch it.(c) Find the test statistic.(d) Make a decision.(e) Use Excel
Cash withdrawals from a college credit union for a random sample of 30 Fridays and 30 Mondays are shown. At 5 .01, is there a difference in the mean withdrawal on Monday and Friday?(a) Make stacked dot plots of the data (a sketch is OK).(b) State the hypotheses.(c) State the decision rule and
In MiniCase 10.2, we found that the mean methane gas emissions for the two pneumatic controller manufacturers were not equal. When choosing formula 10.3 to calculate the t statistic, we assumed that their variances were not equal. Was this a valid assumption? Use Cemco's sample s1 = 147.2 scfd (n1
A ski company in Vail owns two ski shops, one on the west side and one on the east side of Vail. Is there a difference in daily average goggle sales between the two stores? Assume equal variances.(a) State the hypotheses for a two-tailed test.(b) State the decision rule for a level of significance
Researchers analyzed 12 samples of two kinds of Stella's decaffeinated coffee. The caffeine in a cup of decaffeinated espresso had a mean of 9.4 mg with a standard deviation of 3.2 mg, while brewed decaffeinated coffee had a mean of 12.7 mg with a standard deviation of 0.35 mg. Assuming unequal
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