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statistics principles and methods
Statistics The Exploration And Analysis Of Data 6th Edition John M Scheb, Jay Devore, Roxy Peck - Solutions
=+10.32 According to a Washington Post-ABC News poll, 331 of 502 randomly selected U.S. adults interviewed said they would not be bothered if the National Security
=+10.30 The article “Irritated by Spam? Get Ready for Spit”(USA Today, November 10, 2004) predicts that “spit,”spam that is delivered via Internet phone lines and cell m as more people turn to 004 poll of 5500 cell kee Group, 20% indi-mercial messages and ads cient evidence that the o have
=+Forty-three percent of the 1000 people responding said that they would favor drafting women if the draft were reinstated. Using a .05 significance level, carry out a test to determine if there is convincing evidence that fewer than half of adult Americans would favor the drafting of women.
=+10.29 The poll referenced in the previous exercise (“Military Draft Study,” AP-Ipsos, June 2005) also included the following question: “If the military draft were reinstated, would you favor or oppose drafting women as well as men?”
=+oppose the reinstatement of a military draft. Is there convincing evidence that the proportion of American adults who oppose reinstatement of the draft is greater than twothirds? Use a significance level of .05.
=+10.28 The article “Poll Finds Most Oppose Return to Draft, Wouldn’t Encourage Children to Enlist” (Associated Press, December 18, 2005) reports that in a random sample of 1000 American adults, 700 indicated that they H0: p 5 .05, n 5 75 H0: p 5 .9, n 5 100 H0: p 5 .6, n 5 210 H0: p 5 .2, n
=+10.27 Assuming a random sample from a large population, for which of the following null hypotheses and sample sizes n is the large-sample z test appropriate:a.b.c.d.
=+10.26 tomers z test o sociated with each of the given values of the test statistic:a. 1.40d. 2.45b. 0.93e. 20.17c. 1.96
=+10.25 Pairs of P-values and significance levels,a, are given. For each pair, state whether the observed P-value leads to rejection of H0 at the given significance level.a. P-value 5 .084, a 5 .05b. P-value 5 .003, a 5 .001c. P-value 5 .498, a 5 .05d. P-value 5 .084, a 5 .10e. P-vf. P-v
=+10.24 For which of the following P-values will the null hypothesis be rejected when performing a level .05 test:a. .001d. .047b. .021e. .148c. .078
=+10.23 Use the definition of the P-value to explain the following:a. Why H0 would certainly be rejected if P-value 5 .0003b. Why H0 would definitely not be rejected if P-value 5.350
=+c. Would you prefer a test with a 5 .01 or a 5 .1? Explain your reasoning
=+b. In the context of this exercise, describe Type I and Type II errors.
=+a. Which of the following pairs of hypotheses should the manufacturer test:or Explain your answer
=+10.22 An automobile manufacturer is considering using robots for part of its assembly process. Converting to robots is an expensive process, so it will be undertaken only if there is strong evidence that the proportion of defective installations is lower for the robots than for human
=+c. Comment on the spokesperson’s last statement that no study can prove the absence of an effect. Do you agree with this statement?
=+b. If the Cancer Institute researchers were incorrect in their conclusion that there is no increased cancer risk associated with living near a nuclear power plant, are they making a Type I or a Type II error? Explain.
=+a. Let p denote the true proportion of the population in areas near nuclear power plants who die of cancer during a given year. The researchers at the Cancer Institute might have considered the two rival hypotheses of the form H0: p 5 value for areas without nuclear facilities Ha: p . value for
=+10.21 The National Cancer Institute conducted a 2-year study to determine whether cancer death rates for areas near nuclear power plants are higher than for areas without nuclear facilities (San Luis Obispo Telegram-Tribune, September 17, 1990). A spokesperson for the Cancer Institute said,
=+b. Would you prefer a significance level of .1 or .01 for your test? Explain.
=+a. Assuming that a mercury concentration of 5 ppm is considered the maximum safe concentration, which of the following pairs of hypotheses would you test:H0: m 5 5 versus Ha: m . 5 or Give the reasons for your choice.
=+10.20 Suppose that you are an inspector for the Fish and Game Department and that you are given the task of determining whether to prohibit fishing along part of the Oregon coast. You will close an area to fishing if it is determined that fish in that region have an unacceptably high mercury
=+b. In this context, describe Type I and Type II errors, and discuss the consequences of each.
=+a. Explain why the alternative hypothesis was chosen to be Ha: p . .1.
=+where p represents the true proportion of defective flares made by this manufacturer. If H0 is rejected, charges of false advertising will be filed against the manufacturer.
=+10.19 ▼ Occasionally, warning flares of the type contained in most automobile emergency kits fail to ignite.A consumer advocacy group wants to investigate a claim against a manufacturer of flares brought by a person who claims that the proportion of defective flares is much higher than the
=+c. From the printed circuit supplier’s point of view, which type of error is considered more serious?
=+b. From the calculator manufacturer’s point of view, which type of error is considered more serious?
=+a. In this context, define Type I and Type II errors.
=+true proportion of defective circuits in the shipment. If the null hypothesis is not rejected, the shipment is accepted, and the circuits are used in the production of calculators.If the null hypothesis is rejected, the entire shipment is returned to the supplier because of inferior quality. (A
=+10.17 A manufacturer of hand-held calculators receives large shipments of printed circuits from a supplier. It is too costly and time-consuming to inspect all incoming circuits, so when each shipment arrives, a sample is selected for inspection. Information from the sample is then used to test
=+b. Would you recommend a test procedure that uses a 5 .10 or one that uses a 5 .01? Explain.
=+p , .9. The appropriate hypotheses are then H0: p 5 .9 versus Ha: p , .9.a. In the context of this problem, describe Type I and Type II errors, and discuss the possible consequences of each.
=+that no repair is identified with a success). Let p denote the true proportion of successes for all sets made by this manufacturer. The agency does not want to claim false advertising unless sample evidence strongly suggests that
=+3 years of operation. A consumer agency wishes to check this claim, so it obtains a random sample of n 5 100 purchasers and asks each whether the set purchased needed repair during the first 3 years after purchase. Let p be the sample proportion of responses indicating no repair (so
=+b. If Pizza Hut is incorrect in its conclusion, is the company making a Type I or a Type II error?10.16 A television manufacturer claims that (at least)90% of its TV sets will need no service during the first
=+all Pizza Hut restaurants, consider using the sample data to decide between H0: m 5 14 and Ha: m . 14.a. Is Pizza Hut’s conclusion consistent with a decision to reject H0 or to fail to reject H0?
=+based on recording sales information for a random sample of Pizza Hut restaurants selected for the marketing trial.With m denoting the mean percentage increase in sales for
=+10.15 ▼ Pizza Hut, after test-marketing a new product called the Bigfoot Pizza, concluded that introduction of the Bigfoot nationwide would increase its sales by more than 14% (USA Today, April 2, 1993). This conclusion was
=+b if the decision is based on DNA testing in which the mother is not tested?
=+c. Ann Landers also stated, “If the mother is not tested, there is a 0.8 percent chance of a false positive.” For the hypotheses given in Part (a), what are the values of a and
=+a, the probability of Type I error, andb, the probability of Type II error?
=+b. Based on the information given, what are the values of
=+: a particular man is not the father In the context of this problem, describe Type I and Type II errors. (Although these are not hypotheses about a population characteristic, this exercise illustrates the definitions of Type I and Type II errors.)
=+a. Consider using the results of DNA paternity testing to decide between the following two hypotheses:H0: a particular man is the father Ha
=+10.14 Ann Landers, in her advice column of October 24, 1994 (San Luis Obispo Telegram-Tribune), described the reliability of DNA paternity testing as follows: “To get a completely accurate result, you would have to be tested, and so would (the man) and your mother. The test is 100 percent
=+b. Based on the quote regarding consequences of the two kinds of error, which type of error does the doctor quoted consider more serious? Explain.
=+a. For the given hypotheses, describe Type I and Type II errors.
=+Type I and Type II errors.) The article “Blurred Line Between Illness, Abuse Creates Problem for Authorities”(Macon Telegraph, February 28, 2000) included the following quote from a doctor in Atlanta regarding the consequences of making an incorrect decision: “If it’s disease, the
=+10.13 Medical personnel are required to report suspected cases of child abuse. Because some diseases have symptoms that mimic those of child abuse, doctors who see a child with these symptoms must decide between two competing hypotheses:H0: symptoms are due to child abuse Ha: symptoms are due
=+d. What aspect of the relationship between the probability of Type I and Type II errors is being described by the statement in the article that if radiologists were less
=+c. Describe a Type II error in the context of this problem, and discuss the consequences of making a Type II error.
=+b. Describe a Type I error in the context of this problem, and discuss the consequences of making a Type I error.
=+a. Would a false-positive (thinking that cancer is present when in fact it is not) be a Type I error or a Type II error?
=+if radiologists were less aggressive in following up on suspicious tests, the rate of false-positives would fall but the rate of missed cancers would rise. Suppose that such a screening test is used to decide between a null hypothesis of H0: no cancer is present and an alternative hypothesis of
=+10.12 Researchers at the University of Washington and Harvard University analyzed records of breast cancer screening and diagnostic evaluations (“Mammogram Cancer Scares More Frequent than Thought,” USA Today, April 16, 1998). Discussing the benefits and downsides of the screening process,
=+amperage is higher than 40, the manufacturer might be liable for damage to an electrical system as a result of fuse malfunction. To verify the mean amperage of the fuses, a sample of fuses is selected and tested. If a hypothesis test is performed using the resulting data, what null and
=+10.11 ▼ Many older homes have electrical systems that use fuses rather than circuit breakers. A manufacturer of 40-amp fuses wants to make sure that the mean amperage at which its fuses burn out is in fact 40. If the mean amperage is lower than 40, customers will complain because the fuses
=+its customers would be encouraged to make longer calls and thus that there would not be a big loss in revenue. Let m denote the true mean length of long-distance calls after the rate reduction. What hypotheses should the phone company test to determine whether the mean length of long-distance
=+10.10 The mean length of long-distance telephone calls placed with a particular phone company was known to be 7.3 min under an old rate structure. In an attempt to be more competitive with other long-distance carriers, the phone company lowered long-distance rates, thinking that
=+10.9 A county commissioner must vote on a resolution that would commit substantial resources to the construction of a sewer in an outlying residential area. Her fiscal decisions have been criticized in the past, so she decides to take a survey of constituents to find out whether they favor
=+10.8 Researchers have postulated that because of differences in diet, Japanese children have a lower mean blood cholesterol level than U.S. children do. Suppose that the mean level for U.S. children is known to be 170. Let m represent the true mean blood cholesterol level for Japanese children.
=+What hypotheses should the program director test to answer the question of interest?
=+daytime programming. A survey of randomly selected viewers is conducted. Let p represent the true proportion of viewers who prefer regular daytime programming.
=+10.7 ▼ A certain television station has been providing live coverage of a particularly sensational criminal trial. The station’s program director wishes to know whether more than half the potential viewers prefer a return to regular H0: p 5 .6 versus Ha: p . .6 H0: p 5 .6 versus Ha: p , .6
=+the resulting data will be used to test the relevant hypotheses. If p represents the true proportion of all faculty that favor a change to plus–minus grading, which of the following pair of hypotheses should the administration test:or Explain your choice.
=+10.6 A certain university has decided to introduce the use of plus and minus with letter grades, as long as there is evidence that more than 60% of the faculty favor the change. A random sample of faculty will be selected, and
=+no evidence of it.’” (MMR is a measles-mumps-rubella vaccine.) In the context of a hypothesis test with the null hypothesis being that MMR does not cause autism, explain why the author could not just conclude that the MMR vaccine does not cause autism.
=+10.5 Consider the following quote from the article “Review Finds No Link Between Vaccine and Autism” (San Luis Obispo Tribune, October 19, 2005): “‘We found no evidence that giving MMR causes Crohn’s disease and/or autism in the children that get the MMR,’ said Tom Jefferson, one of
=+b. Does the stated conclusion indicate that the null hypothesis was rejected or not rejected? Explain.
=+Ha: concealed weapons laws reduce crime Explain.
=+10.4 Do state laws that allow private citizens to carry concealed weapons result in a reduced crime rate? The author of a study carried out by the Brookings Institution is reported as saying, “The strongest thing I could say is that I don’t see any strong evidence that they are reducing
=+. The inspection team decides to test versus . Explain why this alternative hypothesis was chosen rather than .
=+x 5 50 welds is selected and tests are conducted on each weld in the sample. Weld strength is measured as the force required to break the weld. Suppose that the specifications state that the mean strength of welds should exceed 100 lb/in.2
=+10.3 To determine whether the pipe welds in a nuclear power plant meet specifications, a random sample of H0: p 5 .1, Ha: p Þ .1 H0: m 5 123, Ha: m 5 125 H0: m 5 123, Ha: m , 123 H0: p 5 .4, Ha: p . .6 H0: m 5 15, Ha: m 5 15
=+10.2 For the following pairs, indicate which do not comply with the rules for setting up hypotheses, and explain why:a.b.c.d.e.
=+10.1 Explain why the statement is not a legitimate hypothesis.
=+b. Using the ladder of transformations of Section 5.4 (see Figure 5.31 and Table 5.5), suggest a transformation that might straighten the plot. Give reasons for your choice of transformation
=+“Calculation of Dosage Regimens of Antimicrobial Drugs for Surgical Prophylaxis” (Journal of the American Veterinary Medicine Association [1984]: 1083–1087):x 5 15 45 90 180 y 32.6 43.3 23.1 16.7 5.7 x 240 360 480 1440 y 6.4 9.2 0.4 0.2
=+5.78 ● The following data on y 5 concentration of penicillin-G in pig’s blood plasma (units per milliliter) and x 5 time (in minutes) from administration of a dose of penicillin (22 mg/kg body weight) appeared in the paper
=+c. Calculate and interpret the value of Pearson’s sample correlation coefficient.
=+y 5 judge’s score and x 5 length of final step (in meters)for a sample of seven divers performing a forward pike with a single somersault:y 7.40 9.10 7.20 7.00 7.30 7.30 7.90 x 1.17 1.17 0.93 0.89 0.68 0.74 0.95
=+5.77 ● The paper “Biomechanical Characteristics of the Final Approach Step, Hurdle, and Take-Off of Elite g y 12,306.58 2 5 10,072.41 g x 5 388.8 g y 5 310.3 g x 2 5 15,338.54 g xy 5 American Springboard Divers” (Journal of Human Movement Studies [1984]: 189–212) gave the following data
=+c. If a fifth observation is made at the value x 5 6, find a value of y for which r , .5.
=+b. If a fifth observation is made at the value x 5 6, find a value of y for which r . .5.
=+a. What is the value of the sample correlation coefficient r?
=+5.76 Consider the four (x, y) pairs (0, 0), (1, 1), (1, 21), and (2, 0).
=+d. Would you use the least-squares line to predict flood damage when depth of flooding is 18 ft? Explain.
=+c. Predict flood damage for a structure subjected to 6.5 ft of flooding.
=+b. Construct a scatterplot, and draw the least-squares line on the plot. Does it look as though a straight line provides an adequate description of the relationship between y and x? Explain.
=+(Journal of Water Resources Planning and Management[1985]: 65–81). The following data on x 5 depth of flooding (feet above first-floor level) and y 5 flood damage (as a percentage of structure value) were obtained using a sample of flood insurance claims:x 1 2 3 4 5 6 7 y 10 14 26 28 29 41 43
=+5.75 ● The relationship between the depth of flooding and the amount of flood damage was examined in the paper“Significance of Location in Computing Flood Damage”
=+d. Delete the first observation, (51.3, 49.3), and calculate the new equation of the least-squares line and the value of r 2 . What do you conclude? (Hint: For the original data, , , , , and .)
=+c. How effectively does a straight line summarize the relationship?
=+b. The investigators fit a least-squares line. The resulting MINITAB output is given in the following:The regression equation is firecon = +11.4 + 1.09 treadcon Predictor Coef Stdev t-ratio p Constant –11.37 12.46 –0.91 0.388 treadcon 1.0906 0.3181 3.43 0.009 s = 4.70 R-sq = 59.5% R-sq(adj) =
=+Firefighter 1 2 3 4 5 x 51.3 34.1 41.1 36.3 36.5 y 49.3 29.5 30.6 28.2 28.0 Firefighter 6 7 8 9 10 x 35.4 35.4 38.6 40.6 39.5 y 26.3 33.9 29.4 23.5 31.6a. Does the scatterplot suggest an approximate linear relationship?
=+expenditure requirements for physically demanding tasks.The paper “Oxygen Consumption During Fire Suppression: Error of Heart Rate Estimation” (Ergonomics [1991]:1469–1474) reported on a study in which x 5 oxygen consumption (in milliliters per kilogram per minute) during a treadmill test
=+5.74 ● An accurate assessment of oxygen consumption provides important information for determining energy 1x 1y a x 2 5 62.600235 a xy 5 1114.5 a y 2 5 57,939 n 5 12 a x 5 22.207 a y 5 793
=+b. If a straight line were fit to the data using least squares, what proportion of variation in raises could be attributed to the approximate linear relationship between raises and evaluations?
=+5.73 The sample correlation coefficient between annual raises and teaching evaluations for a sample of n 5 353 college faculty was found to be r 5 .11 (“Determination of Faculty Pay: An Agency Theory Perspective,” Academy of Management Journal [1992]: 921–955).a. Interpret this value.
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