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Applied Statistics In Business And Economics 4th Edition David Doane, Lori Seward - Solutions

A random sample of 21 nickels measured with a very accurate micrometer showed a mean diameter of 0.834343 inch with a standard deviation of 0.001886 inch.(a) Why would nickel diameters vary?(b) Construct a 99 percent confidence interval for the true mean diameter of a nickel.(c) Discuss any
A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were(a) Construct a 90 percent confidence interval for the true mean weight.(b) What sample size would be necessary to estimate the true weight with an error of
Statistics students were asked to go home and fill a 1-cup measure with raisin bran, tap the cup lightly on the counter three times to settle the contents, if necessary add more raisin bran to bring the contents exactly up to the 1-cup line, spread the contents on a large plate, and count the
A sample of 20 pages was taken without replacement from a Yellow Pages directory that has 1,591 pages.(a) Calculate the FPCF for this sample.(b) Should the population be considered effectively in finite?
Twenty-five blood samples were selected by taking every seventh blood sample from racks holding 187 blood samples from the morning draw at a medical center.(a) Calculate the FPCF for this sample.(b) Should the population be considered effectively in finite?
A sample of 20 pages was taken from a Yellow Pages directory. On each page, the mean area devoted to display ads was measured (a display ad is a large block of multicolored illustrations, maps, and text). The data (in square millimeters) are shown below:(a) Construct a 95 percent confidence
8.67 Sixteen owners of 2010 Audi A4 sedans kept track of their average fuel economy for a month. The results are shown below.(a) Construct a 95 percent confidence interval for the mean.(b) What factor(s) limit the conclusions that can be drawn about the true mean?
8.68 Twenty-five blood samples were selected by taking every seventh blood sample from racks holding 187 blood samples from the morning draw at a medical center. The white blood count (WBC) was measured using a Coulter Counter Model S. The mean WBC was 8.636 with a standard deviation of 3.9265.(a)
Twenty-one warranty repairs were selected from a population of 126 by selecting every sixth item. The population consisted of "loose, not attached" minivan electrical wires (one of several electrical failure categories the dealership mechanic can select). The mean repair cost was $45.664 with a
The fat content of a pouch of Keebler Right Bites © Fudge Shoppe © Mini-Fudge Stripes is normally distributed with a mean of 3.50 grams. Assume a known standard deviation of - 0.25 gram.(a) What is the standard error of X-bar, the mean weight from a random sample of 10 pouches of cookies?(b)
Dave the jogger runs the same route every day (about 2.2 miles). On 18 consecutive days, he recorded the number of steps using a pedometer. The results were(a) Construct a 95 percent confidence interval for the true mean number of steps Dave takes on his run.(b) What sample size would be needed to
A pediatrician's records showed the mean height of a random sample of 25 girls at age 12 months to be 29.530 inches with a standard deviation of 1.0953 inches.(a) Construct a 95 percent confidence interval for the true mean height.(b) What sample size would be needed for 95 percent confidence and
A random sample of 10 exam scores showed a standard deviation of 7.2 points. Find the 95 percent confidence interval for the population standard deviation. Use Appendix E to obtain the values of X2L and X2U.
A random sample of 30 lunch orders at Noodles and Company showed a standard deviation of $5.31. Find the 90 percent confidence interval for the population standard deviation. Use Excel to obtain X2L = CHISQ.INV(α/2,d.f.) and X2U = CHISQ.INV.RT( /2,d.f.)
During the Rose Bowl, the length (in seconds) of 12 randomly chosen commercial breaks during timeouts (following touchdown, turnover, field goal, or punt) wereAssuming a normal population, construct a 90 percent confidence interval for the mean TimeOuts length of a commercial break during the Rose
A sample of 40 CDs from a student's collection showed a mean length of 52.74 minutes with a standard deviation of 13.21 minutes.(a) Construct a 95 percent confidence interval for the mean.(b) Why might the normality assumption be an issue here?(c) What sample size would be needed to estimate with
The Environmental Protection Agency (EPA) requires that cities monitor over 80 contaminants in their drinking water. Samples from the Lake Huron Water Treatment Plant gave the results shown here. Only the range is reported, not the mean. For each substance, estimate the standard deviation by using
In a sample of 100 Planter's Mixed Nuts, 19 were found to be almonds.(a) Construct a 90 percent confidence interval for the true proportion of almonds.(b) May normality be assumed? Explain.(c) What sample size would be needed for 90 percent confidence and an error of ±0.03?(d) Why would a quality
A study showed that fourteen of 180 publicly traded business services companies failed a test for compliance with Sarbanes-Oxley requirements for financial records and fraud protection. Assuming that these are a random sample of all publicly traded companies, construct a 95 percent confidence
Concerns about climate change and CO2 reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 35 blended fuels are tested in a lab to ascertain the bio/total carbon ratio.(a) If the true mean is
Noodles & Company wants to estimate the percent of customers who order dessert, with 95 percent confidence and an error of ±10%. What is the required sample size?
Junior Achievement and Deloitte commissioned a "teen ethics poll" of 787 students aged 1318, finding that 29 percent felt inadequately prepared to make ethical judgments.(a) Assuming that this was a random sample, find the 95 percent confidence interval for the true proportion of U.S. teens who
A certain brand of dry noodles contains a mixture of beet, spinach, carrot, and plain. A random sample of 200 dry noodles contained 47 beet noodles.(a) Construct a 95 percent confidence interval for the true proportion of beet noodles.(b) Check the normality assumption for p. Show your work.(c)
CBS asked a sample of DVR owners to record Late Night with David Letterman on their DVRs. Of the 125 DVR owners surveyed, 83 either "gave up or screwed up" because they did not understand how to program the DVR. Construct a 90 percent confidence interval for the true proportion of DVR owners who
A survey of 4,581 U.S. households that owned a mobile phone found that 58 percent are satisfied with the coverage of their cellular phone provider. Assuming that this was a random sample, construct a 90 percent confidence interval for the true proportion of satisfied U.S. mobile phone owners.
A "teen ethics poll" was commissioned by Junior Achievement and Deloitte. The survey by Harris Interactive surveyed 787 students aged 1318.(a) Assuming that this was a random sample of all students in this age group, find the margin of error of the poll.(b) Would the margin of error be greater or
Biting an unpopped kernel of popcorn hurts! As an experiment, a self-confessed connoisseur of cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the unpopped kernels were counted. There were 86.(a) Construct a 90 percent confidence interval for the proportion of
A sample of 213 newspaper tire ads from several Sunday papers showed that 98 contained a low-price guarantee (offer to "meet or beat any price").(a) Assuming that this was a random sample, construct a 95 percent confidence interval for the proportion of all Sunday newspaper tire ads that contain a
A physician's billing office conducted a random check of patient records and found that 36 of 50 patients had changed insurance plans within the past year. Construct a 90 percent confidence interval for the true proportion.
Of 250 college students taking a statistics class, 4 reported an allergy to peanuts.(a) Is the criterion for normality of p met?(b) Assuming that this was a random sample, use MINITAB to construct a 95 percent confidence interval for the proportion of all college statistics students with a peanut
Find a confidence interval for assuming that each sample is from a normal population.a. x-bar = 14, σ = 4, n = 5, 90 percent confidenceb. x-bar = 37, σ = 5, n = 15, 99 percent confidence c. x-bar = 121, σ = 15, n = 25, 95 percent confidence
(a) A poll of 2,277 likely voters was conducted on the president's performance. Approximately what margin of error would the approval rating estimate have?(b) The poll showed that 44 percent approved the president's performance. Construct a 90 percent confidence interval for the true proportion.(c)
To determine the proportion of taxpayers who prefer ling tax returns electronically, a survey of 600 taxpayers was conducted. Calculate the margin of error used to estimate this proportion. What assumptions are required to find the margin of error?
A sample of 40 CDs from a student's collection showed a mean length of 52.74 minutes with a standard deviation of 13.21 minutes. Construct a 95 percent confidence interval for the population standard deviation. (Data are from a project by statistics students Michael Evatz, Nancy Petack, and
Vail Resorts would like to send a survey to their guests asking about their satisfaction with the new 2009 website design. They would like to have a margin of error of 65 percent on responses with 95 percent confidence.(a) Using the conservative approach, what sample size is needed to ensure this
If you repeated a hypothesis test 1,000 times (in other words, 1,000 different samples from the same population), how many times would you expect to commit a Type I error, assuming the null hypothesis were true, if (a) α = .05; (b) α = .01; or (c) α = .001?
A quality standard says that no more than 2 percent of the eggs sold in a store may be cracked (not broken, just cracked). In 3 cartons (12 eggs each carton), 2 eggs are cracked. (a) At the .10 level of significance, does this prove that the standard is exceeded? (b) Calculate a p-value for the
An experimental medication is administered to 16 people who suffer from migraines. After an hour, 10 say they feel better. Is the medication effective (i.e., is the percent who feel better greater than 50 percent)? Use α = .10, explain fully, and show all steps.
The historical on-time percentage for Amtrak's Sunset Limited is 10 percent. In July, the train was on time 0 times in 31 runs. At the .10 level of significance, has the on-time percentage fallen? Explain clearly. Use Excel to calculate the cumulative binomial probability P(X ≤ 0 | n = 31, π =
After 7 months, none of 238 angioplasty patients who received a drug-coated stent to keep their arteries open had experienced restenosis (re-blocking of the arteries). (a) Use MINITAB to construct a 95 percent binomial confidence interval for the proportion of all angioplasty patients who
A certain brand of at white interior latex paint claims one-coat coverage of 400 square feet per gallon. The standard deviation is known to be 20. A sample of 16 gallons is tested.(a) At α = .05 in a left-tailed test, find the risk and power assuming that the true mean is really 380 square feet
A process is normally distributed with standard deviation 12. Samples of size 4 are taken. Suppose that you wish to test the hypothesis that μ = 500 at α = .05 in a left-tailed test.(a) What is the risk if the true mean is 495? If the true mean is 490? If the true mean is 485? If the true mean is
Is this sample of 25 exam scores inconsistent with the hypothesis that the true variance is 64 (i.e., Ïƒ = 8)? Use the 5 percent level of significance in a two-tailed test. Show all steps, including the hypotheses and critical values from Appendix E.
Hammermill Premium Inkjet 24 lb. paper has a specified brightness of 106.(a) At Î± = .005, does this sample of 24 randomly chosen test sheets from a day's production run show that the mean brightness exceeds the specification?(b) Does the sample show that Ïƒ2, 0.0025? State the hypotheses and
Sketch a diagram of the decision rule for each pair of hypotheses.a. H0: μ ≥ 80 versus H1: μ < 80b. H0: μ = 80 versus H1: μ ≠ 80c. H0: μ ≤ 80 versus H1: μ > 80
Find the z calc test statistic for each hypothesis test.a. x-bar = 242, μ0 = 230, σ = 18, n = 20b. x-bar = 3.44, μ0 = 3.50, σ = 0.24, n = 40c. x-bar = 21.02, μ0 = 20.00, σ = 2.52, n = 30
Use Excel to find the critical value of z for each hypothesis test. a. 10 percent level of significance, two-tailed test b. 1 percent level of significance, right-tailed test c. 5 percent level of significance, left-tailed test
Use Excel to find the critical value of z for each hypothesis test. a. α = .05, two-tailed test b. α = .10, right-tailed test c. α = .01, left-tailed test
Find the z calc test statistic for each hypothesis test.a. x-bar = 423, μ0 = 420, σ = 6, n = 9b. x-bar = 8330, μ0 = 8,344, σ = 48, n = 36c. x-bar = 3.102, μ0 = 3.110, σ = .250, n = 25
GreenBeam Ltd. claims that its compact fluorescent bulbs average no more than 3.50 mg of mercury. A sample of 25 bulbs shows a mean of 3.59 mg of mercury.(a) Write the hypotheses for a right-tailed test, using GreenBeam's claim as the null hypothesis about the mean.(b) Assuming a known standard
The mean potassium content of a popular sports drink is listed as 140 mg in a 32-oz bottle. Analysis of 20 bottles indicates a sample mean of 139.4 mg.(a) Write the hypotheses for a two-tailed test of the claimed potassium content.(b) Assuming a known standard deviation of 2.00 mg, calculate the z
Calculate the test statistic and p-value for each sample.a. H0: μ = 60 versus H1: μ ≠ 60, α = .025 x-bar = 63, σ = 8, n = 16b. H0: μ ≥ 60 versus H1: μ < 60, α = .025 x-bar = 58, σ = 8, n = 25c. H0: μ ≤ 60 versus H1: μ > 60, α = .025 x-bar = 65, σ = 8, n = 36
Define Type I and Type II error for each scenario, and identify the cost(s) of each type of error. a. A 25-year-old ER patient in Minneapolis complains of chest pain. Heart attacks in 25-year-olds are rare, and beds are scarce in the hospital. The null hypothesis is that there is no heart attack
Determine the p-value for each test statistic. a. Right-tailed test, z = 11.34 b. Left-tailed test, z = 22.07 c. Two-tailed test, z = 21.69
Procyon Mfg. produces tennis balls. Weights are supposed to be normally distributed with a mean of 2.035 ounces and a standard deviation of 0.002 ounce. A sample of 25 tennis balls shows a mean weight of 2.036 ounces. At α = .025 in a right-tailed test, is the mean weight heavier than it is
The mean arrival rate of fights at O'Hare Airport in marginal weather is 195 fights per hour with a historical standard deviation of 13 fights. To increase arrivals, a new air traffic control procedure is implemented. In the next 30 days of marginal weather, the mean arrival rate is 200 fights per
An airline serves bottles of Galena Spring Water that are supposed to contain an average of 10 ounces. The filling process follows a normal distribution with process standard deviation 0.07 ounce. Twelve randomly chosen bottles had the weights shown below (in ounces).(a) Set up a two-tailed
The Scottsdale re department aims to respond to recalls in 4 minutes or less, on average. Response times are normally distributed with a standard deviation of 1 minute. Would a sample of 18 re calls with a mean response time of 4 minutes 30 seconds provide sufficient evidence to show that the goal
The lifespan of xenon metal halide arc-discharge bulbs for aircraft landing lights is normally distributed with a mean of 3,000 hours and a standard deviation of 500 hours. If a new bal- last system shows a mean life of 3,515 hours in a test on a sample of 10 prototype new bulbs, would you conclude
Discuss the issues of statistical significance and practical importance in each scenario. a. A process for producing I-beams of oriented strand board used as main support beams in new houses has a mean breaking strength of 2,000 lbs./ft. A sample of boards from a new process has a mean breaking
The target activation force of the buttons on a keyless entry clicker is 1.967 newtons. Variation exists in activation force due to the nature of the manufacturing process. A sample of 9 clickers showed a mean activation force of 1.88 newtons. The standard deviation is known to be 0.145 newton. Too
Find the t calc test statistic for each hypothesis test.a. x-bar = 14.7, μ0 = 13.0, s = 1.8, n = 12b. x-bar = 241, μ0 = 250, s = 12, n = 8c. x-bar = 2,102, μ0 = 2,000, s = 242, n = 17
Find the critical value of Student's t for each hypothesis test. a. 10 percent level of significance, two-tailed test, n = 21 b. 1 percent level of significance, right-tailed test, n = 9 c. 5 percent level of significance, left-tailed test, n = 28
A firm decides to test its employees for illegal drugs. (a) State the null and alternative hypotheses. (b) De ne Type I and II errors. (c) What are the consequences of each type of error, and to whom?
Find the critical value of Student's t for each hypothesis test. a. Two-tailed test, n = 18, α = .05 b. Right-tailed test, n = 15, α = .10 c. Left-tailed test, n = 31, α = .01
Find the t calc test statistic for each hypothesis test. a. x-bar = 347, μ0 5 349, s = 1.8, n = 9 b. x-bar = 45, μ0 5 50, s = 12, n = 16 c. x-bar = 4.103, μ0 5 4.004, s = 0.245, n = 25
Estimate the p-value as a range using Appendix D (not Excel): a. t = 1.457, d.f. = 14, right-tailed test b. t = 2.601, d.f. = 8, two-tailed test c. t = 21.847, d.f. = 22, left-tailed test
Find the p-value using Excel (not Appendix D):a. t = 1.457, d.f. = 14, right-tailed testb. t = 2.601, d.f. = 8, two-tailed testc. t = 21.847, d.f. = 22, left-tailed test
Use Excel to find the p-value for each test statistic. a. Right-tailed test, t = + 1.677, n = 13 b. Left-tailed test, t = – 2.107, n = 5 c. Two-tailed test, t = – 1.865, n = 34
Calculate the test statistic and p-value for each sample. State the conclusion for the specifieda. H0: μ = 200 versus H1: μ ≠ 200, α = .025, x-bar = 203, s = 8, n = 16b. H0: μ ≥ 200 versus H1: μ < 200, α = .05, x-bar = 203, s = 5, n = 25c. H0: μ ≤ 200 versus H1: μ > 200, α =
The manufacturer of an airport baggage scanning machine claims it can handle an average of 530 bags per hour. At α = .05 in a left-tailed test, would a sample of 16 randomly chosen hours with a mean of 510 and a standard deviation of 50 indicate that the manufacturer's claim is overstated?
The manufacturer of Glo-More at white interior latex paint claims one-coat coverage of 400 square feet per gallon on interior walls. A painter keeps careful track of 6 gallons and finds coverage (in square feet) of 360, 410, 380, 360, 390, 400.(a) At α = .10 does this evidence contradict the
The average weight of a package of rolled oats is supposed to be at least 18 ounces. A sample of 18 packages shows a mean of 17.78 ounces with a standard deviation of 0.41 ounce.(a) At the 5 percent level of significance, is the true mean smaller than the specification? Clearly state your
According to J.D. Power & Associates, the mean purchase price of a smartphone device (such as an iPhone or Blackberry) in 2008 was $216. In 2009, a random sample of 20 business managers who owned a smartphone device showed a mean purchase price of $209 with a sample standard deviation of
A hotel installs smoke detectors with adjustable sensitivity in all public guest rooms. (a) State the null and alternative hypotheses. (b) De ne Type I and II errors. (c) What are the consequences of each type of error, and to whom?
The average age of a part-time seasonal employee at a Vail Resorts ski mountain has historically been 37 years. A random sample of 50 part-time seasonal employees in 2010 had a sample mean age of 38.5 years with a sample standard deviation equal to 16 years. At the 10 percent level of significance,
The number of entrees purchased in a single order at a Noodles & Company restaurant has had an historical average of 1.60 entrees per order. On a particular Saturday afternoon, a random sample of 40 Noodles orders had a mean number of entrees equal to 1.80 with a standard deviation equal to
In 2008, a small dealership leased 21 Suburu Outbacks on 2-year leases. When the cars were returned in 2010, the mileage was recorded (see below). Is the dealer's mean significantly greater than the national average of 30,000 miles for 2-year leased vehicles, using the 10 per- cent level of
At Oxnard University, a sample of 18 senior accounting majors showed a mean cumulative GPA of 3.35 with a standard deviation of 0.25.(a) At α = .05 in a two-tailed test, does this differ significantly from 3.25 (the mean GPA for all business school seniors at the university)?(b) Use the sample to
Interpret each p-value in your own words:a. p-value = .387, H0 : π ≥ .20, H1: π < .20, α = .10b. p-value = .043, H0 : π ≥ .90, H1: π < .90, α = .05c. p-value = .0012, H0 : π ≥ .50, H1: π < .50, α = .01
Calculate the test statistic and p-value for each sample.a. H0: π = .20 versus H1: π ≠ 20, α = .025, p = .28, n = 100b. H0: π ≤ .20 versus H1: π > 50, α = .025, p = .60, n = 90c. H0: π ≤ .20 versus H1: π > .75, α = .10, p = .28, n = 50
Calculate the test statistic and p-value for each sample.a. H0: π ≤ .60 versus H1: π > .60, α = .05, x = 56, n = 80b. H0: π = .60 versus H1: π ≠ .60, α = .05, x = 56, n = 40c. H0: π ≥ .60 versus H1: π < .60, α = .05, x = 56, n = 100
May normality of the sample proportion p be assumed? Show your work. a. H0: π = .30 versus H1: π ≠ .30, n = 20 b. H0: π = .05 versus H1: π ≠ .60, n = 80 c. H0: π = .10 versus H1: π ≠ .60, n = 80
In a recent survey, 10 percent of the participants rated Pepsi as being "concerned with my health." PepsiCo's response included a new "Smart Spot" symbol on its products that meet certain nutrition criteria, to help consumers who seek more healthful eating options. At α = .05, would a follow-up
In a hospital's shipment of 3,500 insulin syringes, 14 were unusable due to defects.(a) At α = .05, is this sufficient evidence to reject future shipments from this supplier if the hospital's quality standard requires 99.7 percent of the syringes to be acceptable? State the hypotheses and decision
What is the consequence of a false negative in an inspection of your car's brakes?
To combat antibiotic resistance, the Quality Improvement Consortium recommends a throat swab to con firm strep throat before a physician prescribes antibiotics to children under age 5. In a random sample of 60 children who received antibiotics for throat infections, 18 did not have a throat
To encourage telephone efficiency, a catalog call center issues a guideline that at least half of all telephone orders should be completed within 2 minutes. Subsequently, a random sample of 64 telephone calls showed that only 24 calls lasted 2 minutes or less.(a) At α = .05 is this a significant
The recent default rate on all student loans is 5.2 percent. In a recent random sample of 300 loans at private universities, there were 9 defaults.(a) Does this sample show sufficient evidence that the private university loan default rate is below the rate for all universities, using a left-tailed
A poll of 702 frequent and occasional fliers found that 442 respondents favored a ban on cell phones in fight, even if technology permits it. At α = .05, can we conclude that more than half the sampled population supports a ban?
A coin was flipped 12 times and came up heads 10 times.(a) Would we be justified in assuming that the sample proportion p is normally distributed? Explain.(b) Calculate a p-value for the observed sample outcome, using the normal distribution. At the .05 level of significance in a right-tailed test,
BriteScreen, a manufacturer of 19-inch LCD computer screens, requires that on average 99.9 percent of all LCDs conform to its quality standard. In a day's production of 2,000 units, 4 are defective. (a) Assuming this is a random sample, is the standard being met, using the 10 percent level of
Perfect pitch is the ability to identify musical notes correctly without hearing another note as a reference. The probability that a randomly chosen person has perfect pitch is .0005.(a) If 20 students at Julliard School of Music are tested, and 2 are found to have perfect pitch, would you conclude
A quality expert inspects 400 items to test whether the population proportion of defectives exceeds .03, using a right-tailed test at α = .10.(a) What is the power of this test if the true proportion of defectives is π = .04?(b) If the true proportion is π = .05?(c) If the true proportion of
Repeat the previous exercise, using lower? α = .05. For each true value of π, is the power higher or lower?Previous exerciseA quality expert inspects 400 items to test whether the population proportion of defectives exceeds .03, using a right-tailed test at α = .10.(a) What is the power of this
For a certain wine, the mean pH (a measure of acidity) is supposed to be 3.50 with a known standard deviation of α = .10. The quality inspector examines 25 bottles at random to test whether the pH is too low, using a left-tailed test at α = .01.(a) What is the power of this test if the true mean
What is the consequence of a false positive in a weekly inspection of a nuclear plant's cooling system?
Repeat the previous exercise, using lower? α = .05. For each true value of, is the power higher or lower?Previous exerciseFor a certain wine, the mean pH (a measure of acidity) is supposed to be 3.50 with a known standard deviation of α = .10. The quality inspector examines 25 bottles at random
A sample of size n = 15 has variance s2 = 35. At α = .01 in a left-tailed test, does this sample contradict the hypothesis that σ2 = 50?
A sample of size n = 10 has variance s2 = 16. At α = .10 in a two-tailed test, does this sample contradict the hypothesis that σ2 = 24?

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