Construct a confidence interval for μ assuming that each sample is from a normal population. a. x bar = 14, σ = 4, n = 5, 90 percent confidence b. x bar = 37, σ = 5, n = 15, 99 percent confidence c. x bar = 121, σ = 15, n = 25, 95 percent confidence
> Between 2 a.m. and 4 a.m. at an all-night pizza parlor, the mean time between arrival of telephone pizza orders is 20 minutes. (a) Find the median wait for pizza order arrivals. (b) Explain why the median is not equal to the mean. (c) Find the upper quar
> Calculate the test statistic and p-value for each sample. a. H0: π < .60 versus H1: π > .60, α = .05, x = 56, n = 80 b. H0: π = .30 versus H1: π ≠ .30, α = .05, x = 18, n = 40 c. H0: π > .10 versus H1: π < .10, α = .01, x = 3, n = 100
> Interpret each p-value in your own words: a. p-value = .387, H0: π > .20, H1: π < .20, α = .10 b. p-value = .043, H0: π < .90, H1: π > .90, α = .05 c. p-value = .0012, H0: π = .50, H1: π ≠ .50, α = .01
> 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 seni
> 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 ye
> A hotel installs smoke detectors with adjustable sensitivity in all public guest rooms. (a) State the null and alternative hypotheses. (b) Define Type I and II errors. (c) What are the consequences of each type of error, and to whom?
> 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 t
> Which type of data (cross-sectional or time series) is each variable? a. Scores of 50 students on a midterm accounting exam last semester. b. Bob’s scores on 10 weekly accounting quizzes last semester. c. Average score by all takers of the state’s CPA e
> Sarah and Bob share a 1,000-minute cell phone calling plan. (a) Make a stacked dot plot to compare the lengths of cell phone calls by Sarah and Bob during the last week. (b) Describe what the dot plots tell you. Sarah’s calls: 1, 1, 1, 1, 2, 3, 3, 3, 5,
> Noodles & Company is interested in testing whether their new menu design helps reduce the average order time for their customers. Suppose that the average order time prior to the introduction of their new menu was 1.2 minutes. Write the hypotheses for a
> A manufacturer claims that its compact fluorescent bulbs contain an average of 2.5 mg of mercury. Write the hypotheses for a two-tailed test, using the manufacturer’s claim about the mean as the null hypothesis.
> A passenger metal detector at Chicago’s Midway Airport gives an alarm 0.5 time a minute. (a) Find the median waiting time until the next alarm. (b) Find the first quartile of waiting time before the next alarm. (c) Find the 30th percentile waiting time u
> 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-tail
> 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 f
> 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?
> 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?
> 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?
> 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 f
> 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 b
> A poll of 702 frequent and occasional fliers found that 442 respondents favored a ban on cell phones in flight, even if technology permits it. At α = .05, can we conclude that more than half the sampled population supports a ban?
> What is the consequence of a false negative in an inspection of your car’s brakes? Hint: The null hypothesis is the status quo (things are OK).
> 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 eati
> Find each uniform continuous probability and sketch a graph showing it as a shaded area. a. P (X < 10) for U (0, 50) b. P (X > 500) for U (0, 1,000) c. P (25 < X < 45) for U (15, 65)
> 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 ≠ .05, n = 50 c. H0: π = .10 versus H1: π ≠ .10, n = 400
> Calculate the test statistic and p-value for each sample. A. H0: π = .20 versus H1: π ≠ .20, α 5 .025, p = .28, n = 100 B. H0: π < .50 versus H1: π > .50, α 5 .025, p = .60, n = 90 C. H0: π < .75 versus H1: π > .75, α 5 .10, p = .82, n = 50
> 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
> 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.
> 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 w
> 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
> Use Excel to find the p-value for each test statistic. a. Right-tailed test, t = 11.677, n = 13 b. Left-tailed test, t = 22.107, n = 5 c. Two-tailed test, t = 21.865, n = 34
> Find the p-value using Excel (not Appendix D): 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 tcalc test statistic for each hypothesis test. A. x bar = 347, μ0 = 349, s = 1.8, n = 9 B. x bar = 45, μ0 = 50, s = 12, n = 16 C. x bar = 4.103, μ0 = 4.004, s = 0.245, n = 25
> Find the critical value of Student’s t for each hypothesis test. a. Two-tailed test, n = 18, a = .05 b. Right-tailed test, n = 15, a = .10 c. Left-tailed test, n = 31, a = .01
> Between 11 p.m. and midnight on Thursday night, Mystery Pizza gets an average of 4.2 telephone orders per hour. (a) Find the median waiting time until the next telephone order. (b) Find the upper quartile of waiting time before the next telephone order.
> 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
> Find the tcalc test statistic for each hypothesis test. A. x bar = 14.7, μ0 = 13.0, s = 1.8, n = 12 B. x bar = 241, μ0 = 250, s = 12, n = 8 C. x bar = 2,102, μ0 = 2,000, s = 242, n = 17
> 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 ballast system shows a mean life of 3,515 hours in a test on a sample of
> 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,
> Determine the p-value for each test statistic. a. Right-tailed test, z = +1.34 b. Left-tailed test, z = -2.07 c. Two-tailed test, z = -1.69
> Green Beam 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 Green Beam’s claim as the null hypothesis
> Find the zcalc test statistic for each hypothesis test. A. x bar = 423, μ0 = 420, σ = 6, n = 9 B. x bar = 8330, μ0 = 8,344, σ = 48, n = 36 C. x bar = 3.102, μ0 = 3.110, σ = .250, n = 25
> 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
> 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
> Find the zcalc test statistic for each hypothesis test. A. x bar = 242, μ0 = 230, σ = 18, n = 20 B. x bar = 3.44, μ0 = 3.50, σ = 0.24, n = 40 C. x bar = 21.02, μ0 = 20.00, σ = 2.52, n = 30
> The time it takes a ski patroller to respond to an accident call has an exponential distribution with an average equal to 5 minutes. (a) In what time will 90 percent of all ski accident calls be responded to? (b) If the ski patrol would like to be able t
> The Ball Corporation’s aluminum can manufacturing facility in Ft. Atkinson, Wisconsin, wants to use a sample to perform a two-tailed test to see whether the mean incoming metal thickness is at the target of 0.2731 mm. A deviation in either direction woul
> Sketch a diagram of the decision rule for each pair of hypotheses. a. H0: μ >80 versus H1: μ < 80 b. H0: μ = 80 versus H1: μ ≠ 80 c. H0: μ < 80 versus H1: μ > 80
> The average age of a part-time seasonal employee at a Vail Resorts ski mountain has historically been 37 years. State the hypotheses one would use to test if this average has decreased since the last season.
> 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 = .0
> The fuel economy of a 2011 Lexus RX 350 2WD 6 cylinder 3.5 L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of μ = 25.0 MPG and a standard deviation of σ = 1.25 MPG. (a) What is the standard error of X , the me
> 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 , the mean weight from a random sam
> (a) Find the standard error of the mean for each sampling situation (assuming a normal population). (b) What happens to the standard error each time you quadruple the sample size? a. σ = 24, n = 9 b. σ = 24, n = 36 c. σ = 24, n = 144
> Find the 90 percent confidence interval for the standard deviation of gasoline mileage mpg for these 16 San Francisco commuters driving hybrid gas-electric vehicles. 38.8 48.9 28.5 40.0 38.8 29.2 29.1 38.5 34.4 46.1 51.8 30.7 36.9 25.6 42.7 38.3
> 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. Construct a 95 percent confidence interval for the population variance. (Data are from a proje
> At a certain Noodles & Company restaurant, customers arrive during the lunch hour at a rate of 2.8 per minute. What is the probability that (a) at least 30 seconds will pass before the net customer walks in; (b) no more than 15 seconds; (c) more than 1 m
> The weights of 20 oranges (in ounces) are shown below. Construct a 95 percent confidence interval for the population standard deviation. Note: Scale was only accurate to the nearest ¼ ounce. (Data are from a project by statistics student Ju
> Find the 95 percent confidence interval for the population variance from these samples. a. n = 15 commuters, s = 10 miles driven b. n = 18 students, s = 12 study hours
> Inspection of a random sample of 19 aircraft showed that 15 needed repairs to fix a wiring problem that might compromise safety. How large a sample would be needed to estimate the true proportion of jets with the wiring problem, with 90 percent confidenc
> What sample size would be needed to estimate the true proportion of American adults who know their cholesterol level, using 95 percent confidence and an error of ±0.02?
> What sample size would be needed to estimate the true proportion of American households that own more than one DVD player, with 90 percent confidence and an error of ±0.02?
> (a) Find the standard error of the mean for each sampling situation (assuming a normal population). (b) What happens to the standard error each time you quadruple the sample size? a. σ = 32, n = 4 b. σ = 32, n = 16 c. σ = 32, n = 64
> The city fuel economy of a 2009 Toyota 4Runner 2WD 6 cylinder 4 L automatic 5-speed using regular gas is a normally distributed random variable with a range 16 MPG to 21 MPG. (a) Estimate the standard deviation using Method 3 (the Empirical Rule for a no
> In an intra-squad swim competition, men’s freestyle 100 swim times at a certain university ranged from 43.89 seconds to 51.96 seconds. (a) Estimate the standard deviation using Method 3 (the Empirical Rule for a normal distribution). (b) What sample size
> Noodles & Company wants to estimate the mean spending per customer at a certain restaurant with 95 percent confidence and an error of ±$0.25. What is the required sample size, assuming a standard deviation of $2.50 (based on similar restaurants elsewhere
> Analysis showed that the mean arrival rate for vehicles at a certain Shell station on Friday afternoon last year was 4.5 vehicles per minute. How large a sample would be needed to estimate this year’s mean arrival rate with 98 percent confidence and an e
> Between 11 p.m. and midnight on Thursday night, Mystery Pizza gets an average of 4.2 telephone orders per hour. Find the probability that (a) at least 30 minutes will elapse before the next telephone order; (b) less than 15 minutes will elapse; and (c) b
> J.D. Power and Associates says that 60 percent of car buyers now use the Internet for research and price comparisons. (a) Find the probability that in a sample of 8 car buyers, all 8 will use the Internet; (b) at least 5; (c) more than 4. (d) Find the me
> Popcorn kernels are believed to take between 100 and 200 seconds to pop in a certain microwave. (a) Estimate σ using Method 3 from Table 8.11. (b) What sample size (number of kernels) would be needed to estimate the true mean seconds to pop wi
> Last year, a study showed that the average ATM cash withdrawal took 65 seconds with a standard deviation of 10 seconds. The study is to be repeated this year. How large a sample would be needed to estimate this year’s mean with 95 percent confidence and
> A random survey of 500 students was conducted from a population of 2,300 students to estimate the proportion who had part-time jobs. The sample showed that 245 had part-time jobs. Calculate the 90 percent confidence interval for the true proportion of st
> A survey showed that 4.8 percent of the 250 Americans surveyed had suffered some kind of identity theft in the past 12 months. (a) Construct a 99 percent confidence interval for the true proportion of Americans who had suffered identity theft in the past
> Of 43 bank customers depositing a check, 18 received some cash back. (a) Construct a 90 percent confidence interval for the proportion of all depositors who ask for cash back. (b) Check the normality assumption of p.
> From a list of stock mutual funds, 52 funds were selected at random. Of the funds chosen, it was found that 19 required a minimum initial investment under $1,000. (a) Construct a 90 percent confidence interval for the true proportion requiring an initial
> In a sample of 500 new websites registered on the Internet, 24 were anonymous (i.e., they shielded their name and contact information). (a) Construct a 95 percent confidence interval for the proportion of all new websites that were anonymous. (b) May nor
> A car dealer is taking a customer satisfaction survey. Find the margin of error (i.e., assuming 95% confidence and π = .50) for (a) 250 respondents, (b) 125 respondents, and (c) 65 respondents.
> Find the margin of error for a poll, assuming that π = .50. a. n = 50 b. n = 200 c. n = 500 d. n = 2,000
> Should p be assumed normal? a. n = 25, π = .50 b. n = 60, π = .20 c. n = 100, π = .08
> For a large Internet service provider (ISP), web virus attacks occur at a mean rate of 150 per day. (a) Estimate the probability of at least 175 attacks in a given day. (b) Estimate the probability of fewer than 125 attacks. (c) Is the normal approximati
> Should p be assumed normal? a. n = 200, π = .02 b. n = 100, π = .05 c. n = 50, π = .50
> Calculate the standard error of the sample proportion. a. n = 40, π = .30 b. n = 200, π = .10 c. n = 30, π = .40 d. n = 400, π = .03
> Calculate the standard error of the sample proportion. a. n = 30, π = .50 b. n = 50, π = .20 c. n = 100, π = .10 d. n = 500, π = .005
> A random sample of 10 shipments of stick-on labels showed the following order sizes. (a) Construct a 95 percent confidence interval for the true mean order size. (b) How could the confidence interval be made narrower? (Data are from a project by MBA stud
> A random sample of monthly rent paid by 12 college seniors living off campus gave the results below (in dollars). Find a 99 percent confidence interval for μ, assuming that the sample is from a normal population. 900 810 770 860 850 79
> A sample of 21 minivan electrical warranty repairs for “loose, not attached” wires (one of several electrical failure categories the dealership mechanic can select) showed a mean repair cost of $45.66 with a standard deviation of $27.79. (a) Construct a
> Find the interval within which 95 percent of the sample means would be expected to fall, assuming that each sample is from a normal population. a. μ = 200, σ = 12, n = 36 b. μ = 1,000, σ = 15, n = 9 c. μ = 50, σ = 1, n = 25
> For each value of d.f. (degrees of freedom), look up the value of Student’s t in Appendix D for the stated level of confidence. Then use Excel to find the value of Student’s t to four decimal places. Which method (Appendix D or Excel) do you prefer, and
> Find a confidence interval for μ assuming that each sample is from a normal population. a. x bar = 24, s = 3, n = 7, 90 percent confidence b. x bar = 42, s = 6, n = 18, 99 percent confidence c. x bar = 119, s = 14, n = 28, 95 percent confidence
> The Ball Corporation’s beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with a known thickness standard deviation σ = .000959 mm. If a random sample of 58 sheets of metal resulted in x = 0.2731 mm, c
> On average, 28 patients per hour arrive in the Foxboro 24-Hour Walk-in Clinic on Friday between 6 p.m. and midnight. (a) What is the approximate probability of more than 35 arrivals? (b) What is the approximate probability of fewer than 25 arrivals? (c)
> Guest ages at a Vail Resorts ski mountain typically have a right-skewed distribution. Assume the standard deviation (σ) of age is 14.5 years. (a) Even though the population distribution of age is right skewed, what will be the shape of the distribution o
> The fuel economy of a 2011 Lexus RX 350 2WD 6 cylinder 3.5 L automatic 5-speed using premium fuel is normally distributed with a known standard deviation of 1.25 MPG. If a random sample of 10 tanks of gas yields a mean of 21.0 MPG, find the 95 percent co
> A random sample of 100 items is drawn from a population whose standard deviation is known to be σ = 50. The sample mean is x bar = 850. a. Construct an interval estimate for μ with 95 percent confidence. b. Repeat part a assuming that σ = 100. c. Repeat
> A random sample of 25 items is drawn from a population whose standard deviation is known to be σ = 40. The sample mean is x bar = 270. a. Construct an interval estimate for μ with 95 percent confidence. b. Repeat part a assuming that n = 50. c. Repeat pa
> Use the sample information x bar = 37, σ = 5, n = 15 to calculate the following confidence intervals for μ assuming the sample is from a normal population: (a) 90 percent confidence; (b) 95 percent confidence; (c) 99 percent confidence. (d) Describe how
> Construct a confidence interval for μ assuming that each sample is from a normal population. a. x bar = 24, σ = 3, n = 10, 90 percent confidence b. x bar = 125, σ = 8, n = 25, 99 percent confidence c. x bar = 12.5, σ = 1.2, n = 50, 95 percent confidence
> If all normal distributions have the same shape, how do they differ?
> Assume the weight of a randomly chosen American passenger car is a uniformly distributed random variable ranging from 2,500 pounds to 4,500 pounds. (a) What is the mean weight of a randomly chosen vehicle? (b) The standard deviation? (c) What is the prob
> For a continuous uniform distribution, why is P(25 < X < 45) the same as P(25 < X < 45)?
> Suppose that the distribution of oil prices ($/bbl) is forecast to be T(50, 65, 105). (a) Find the mean. (b) Find the standard deviation. (c) Find the probability that the price will be greater than $75. (d) Sketch the distribution and shade the area for
> When confronted with an in-flight medical emergency, pilots and crew can consult staff physicians at a global response center located in Arizona. If the global response center is called, there is a 4.8 percent chance that the flight will be diverted for
