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Statistics 12th Edition James T. McClave, Terry T Sincich - Solutions

In a paper presented at the 2000 Conference of the International Association for Time Use Research professor Margaret Sanik of Ohio State University reported the results of her study on American cable TV viewers who purchase items from one of the home shopping channels. She found that the average
For each of the rejection regions defined in Exercise 8.59, what is the probability that a Type I error will be made? In Exercise 8.59 For each of the following rejection regions, sketch the sampling distribution of t and indicate the location of the rejection region on your sketch: a. t > 1.440,
The following sample of six measurements was randomly selected from a normally distributed population: 1, 3, -1, 5, 1, 2.a. Test the null hypothesis that the mean of the population is 3 against the alternative hypothesis, µ < 3. Use α = .05.b. Test the null hypothesis that the mean of the
Suppose you conduct a t -test for the null hypothesis H0:µ = 1,000 versus the alternative hypothesis Ha: µ = 1,000, based on a sample of 17 observations. The test results are t = 1.89, p-value = .038. a. What assumptions are necessary for the validity of this procedure? b. Interpret the
Refer to the Reading in a Foreign Language (April 2004) experiment to improve the Japanese reading comprehension levels of University of Hawaii students presented in Exercise. Recall that 14 students participated in a 10-week extensive reading program in a second-semester Japanese course. The data
Refer to the Behavioral Ecology (Jan. 2005) experiment on crab spiders' use of camouflage to hide from predators (e.g., birds) on flowers, presented in Exercise. Researchers at the French Museum of Natural History collected a sample of 10 adult female crab spiders, each sitting on the yellow
Amusia is a congenital disorder that adversely impacts one's perception of music. Refer to the Advances in Cognitive Psychology (Vol. 6, 2010) study of the pitch memory of individuals diagnosed with amusia, Exercise. Recall that each in a sample of 17 amusiacs listened to a series of tone pairs and
When bonding teeth, ortho dontists must maintain a dry field. A new bonding adhesive (called "Smartbond") has been developed to eliminate the necessity of a dry field. However, there is concern that the new bonding adhesive is not as strong as the current standard, a composite adhesive. (Trends in
Refer to the Journal of Biogeography (December 2003) study of ants in Mongolia (central Asia), presented in Exercise. Recall that botanists placed seed baits at 11 study sites and observed the number of ant species attracted to each site.A portion of the data (saved in the GOBIANTS file) is
One of the most feared predators in the ocean is the great white shark. It is known that the white shark grows to a mean length of 21 feet; however, one marine biologist believes that great white sharks off the Bermuda coast grow much longer owing to unusual feeding habits. To test this claim, some
Suppose a random sample of 100 observations from a binomial population gives a value of p = .69 and you wish to test the null hypothesis that the population parameter p is equal to .75 against the alternative hypothesis that p is less than .75.a. Noting that p = .69, what does your intuition tell
A random sample of 100 observations is selected from a binomial population with unknown probability of success, p. The computed value of p > is equal to .74.a. Test H0: p = .65 against Ha: p > .65. Use a = .01.b. Test H0: p = .65 against Ha: p > .65. Use a = .10.c. Test H0: p = .90 against
A spokesperson for the National Association of Broadcasters (NAB) claims that 80% of all satellite radio subscribers have a satellite radio receiver in their car. Recall from Exercise, that in a June 2007 survey of 501 satellite radio subscribers, 396 had a satellite receiver in their car. Consider
Chance (Winter 2010) presented a lesson in hypothesis testing carried out by medical students in a biostatistics class. Students were blind-folded and then given a red-colored or yellow-colored gummy bear to chew. (Half the students were randomly assigned to receive the red gummy bear and half to
Refer to the Pew Internet and American Life Project (April 2008) survey of the writing habits of U.S. teenagers, Exercise. Recall that in a random sample of 700 teenagers, 448 admitted to using at least one informal element in school writing assignments. Is there evidence to indicate that less than
Are student-athletes at Division I universities poorer students than non-athletes? The National Collegiate Athletic Association (NCAA) measures the academic outcomes of student-athletes with the Graduation Success Rate (GSR)-the percentage of eligible athletes who graduate within six years of
Meteoritics (March 1995) reported the results of a study of lunar soil evolution. Data were obtained from the Apollo 16 mission to the moon, during which a 62-cm core was extracted from the soil near the landing site.Monomineralic grains of lunar soil were separated out and examined for coating
A group of Australian entomological toxicologists investigated the impact of exposure to low oxygen on the mortality of insects (Journal of Agricultural, Biological, and Environmental Statistics, Sept. 2000). Thousands of adult rice weevils were placed in a chamber filled with wheat grain, and the
Define the power of a test.
List three factors that will increase the power of the test.
Refer to Exercise 8.99.a. If µ = 1,040 instead of 1,020, what is the probability that the hypothesis test will incorrectly fail to reject H0? That is, what is b?b. If µ = 1,040, what is the probability that the test will correctly reject the null hypothesis? That is, what is the power of the
Refer to Exercise 8.101.a. Find b for each of the following values of the population mean: 49, 47, 45, 43, and 41.b. Plot each value of b you obtained in part a against its associated population mean. Show b on the vertical axis and µ on the horizontal axis. Draw a curve through the five points on
Refer to the Current Allergy & Clinical Immunology study of health care workers diagnosed with a latex allergy, Exercise. You tested the null hypothesis of µ = 20 against the alternative hypothesis of µ = 20 using α = .01, where µ is the mean number of latex gloves used per week. The sample of
According to the Environmental Protection Agency (EPA) Fuel Economy Guide, the 2009 Honda Civic automobile obtains a mean of 36 miles per gallon (mpg) on the highway. Suppose Honda claims that the EPA has underestimated the Civic's mileage. To support its assertion, the company selects n = 50 model
Refer to the National Association of Broadcasters (NAB) survey of 501 satellite radio subscribers, Exercise. Recall that an NAB spokesperson claims that 80% of all satellite radio subscribers have a satellite radio receiver in their car. You conducted a test to determine if the claimed value is too
True or False. The null hypotheses H0: σ2 = .25 and H0: σ = .5 are equivalent.
Let x02 be a particular value of x2. Find the value of x02 such that a. P(x2 > x02) = .10 for n = 12 b. P(x2 > x02) = .05 for n = 9 c. P(x2 > x02) = .025 for n = 5
A random sample of seven measurements gave x = 9.4 and σ2 = 1.84.a. What assumptions must you make concerning the population in order to test a hypothesis about σ2?b. Suppose the assumptions in part a are satisfied. Test the null hypothesis σ2 = 1 against the alternative hypothesis σ2 > 1.
A random sample of n = 7 observations from a normal population produced the following measurements: 4, 0, 6, 3, 3, 5, 9. Do the data provide sufficient evidence to indicate that σ2 < 2? Test, using α = .05.
Refer to the Trends in Biomaterials & Artificial Organs (January 2003) study of a new bonding adhesive for teeth called "Smartbond," presented in Exercise. Recall that tests on a sample of 10 extracted teeth bonded with the new adhesive resulted in a mean breaking strength (after 24 hours) of x
Refer to the Geographical Analysis (Oct. 2006) study of a new method for analyzing remote-sensing data from satellite pixels, presented in Exercise 8.32 (p. 365). Recall that the method uses a numerical measure of the distribution of gaps, or the sizes of holes, in the pixel, called lacunarity.
Refer to the Journal of Biogeography (December 2003) study of ants in Mongolia (central Asia), presented in Exercise. Data on the number of ant species attracted to 11 randomly selected desert sites are saved in the GOBIANTS file. Do these data indicate that the standard deviation of the number of
Refer to the Journal of Engineering for Gas Turbines and Power (Jan. 2005) study of the performance of augmented gas turbine engines, presented in Exercise. Recall that the performance of each in a sample of 67 gas turbines was measured by heat rate (kilojoules per kilowatt per hour). The data are
Refer to the Applied Psychology in Criminal Justice (Sept. 2009) study of the personality characteristics of convicted drug dealers, Exercise. A random sample of 100 drug dealers had a mean Wanting Recognition (WR) score of 39 points, with a standard deviation of 6 points. Recall that the WR score
Specify the differences between a large-sample and small sample test of hypothesis about a population mean m. Focus on the assumptions and test statistics.
A random sample of 20 observations selected from a normal population produced x = 72.6 and s2 = 19.4.a. Form a 90% confidence interval for m.b. Test H0:µ= 80 against Ha: µ< 80. Use α = .05.c. Test H0:µ= 80 against Ha: µ≠ 80. Use α = .01.d. Form a 99% confidence interval for m.e. How
A random sample of 175 measurements possessed a mean of x = 8.2 and a standard deviation of s = .79.a. Form a 95% confidence interval for m.b. Test H0:µ= 8.3 against Ha: µ ≠ 8.3. Use α = .05.c. Test H0:µ= 8.4 against Ha: µ ≠ 8.4. Use α = .05.
A t -test is conducted for the null hypothesis H0:µ= 10 versus the alternative hypothesis Ha: µ ≠ 10 for a random sample of n = 17 observations. The test results are t = 1.174 and p-value = .1288. a. Interpret the p -value. b. What assumptions are necessary for the validity of this test? c.
When a new drug is formulated, the pharmaceutical company must subject it to lengthy and involved testing before receiving the necessary permission from the Food and Drug Administration (FDA) to market the drug. The FDA requires the pharmaceutical company to provide substantial evidence that the
Refer to the U.S. Department of Transportation study of the level of cell phone use by drivers while they are in the act of driving a motor passenger vehicle, presented in Exercise 7.119 (p. 342). Recall that in a random sample of 1,165 drivers selected across the country, 35 were found using their
"Take the Pepsi Challenge" was a marketing campaign used by the Pepsi-Cola Company. Coca-Cola drinkers participated in a blind taste test in which they tasted unmarked cups of Pepsi and Coke and were asked to select their favorite. Pepsi claimed that "in recent blind taste tests, more than half the
Medical tests have been developed to detect many serious diseases. A medical test is designed to minimize the probability that it will produce a "false positive" or a "false negative." A false positive is a positive test result for an individual who does not have the disease, whereas a false
Using van-mounted state of-the-art video technology, the Mississippi Department of Transportation collected data on the number of cracks (called crack intensity) in an undivided two-lane highway. (Journal of Infrastructure Systems, March 1995). The mean number of cracks found in a sample of eight
A marine biologist wishes to use parrot fish for experimental purposes due to the belief that their weight is fairly stable (i.e., the variability in weights among parrot fish is small). The biologist randomly samples 10 parrot fish and finds that their mean weight is 4.3 pounds and the standard
Refer to Exercise 8.153.a. In the context of the problem, define a Type II error.b. Calculate b for the test described in part a of Exercise 8.153, assuming that the true mean is µ = 3.1 ppm.c. What is the power of the test to detect the effluent's departure from the standard of 3.0 ppm when the
Refer to the Journal of the American Law and Economics Association (Vol. 3, 2001) study of appeals of federal civil trials, presented in Exercise. A breakdown of 678 civil cases that were originally tried in front of a judge and appealed by either the plaintiff or the defendant is reproduced in the
Ophthalmologists require an instrument that can rapidly measure interocular pressure for glaucoma patients. The device now in general use is known to yield readings of this pressure with a variance of 10.3. The variance of five pressure readings on the same eye by a newly developed instrument is
In Exercise 4.128 (p. 219) you read about a nationwide survey which claimed that 60% of parents with young children condone spank ing their child as a regular form of punishment (Tampa Tribune , October 5, 2000). In a random sample of 100 parents with young children, how many parents would need to
"Hot Tamales" are chewy, cinna mon-flavored candies. A bulk vending machine is known to dispense, on average, 15 Hot Tamales per bag. Chance (Fall 2000) published an article on a classroom project in which students were required to purchase bags of Hot Tamales from the machine and count the number
In each case, determine whether the sample sizes are large enough to conclude that the sampling distribution of (p̂1 - p̂2) is approximately normal. a. n1 = 10, n2 = 12, p̂1 = .50, p̂2 = .50 b. n1 = 10, n2 = 12, p̂1 = .10, p̂2 = .08 c. n1 = n2 = 30, p̂1 = .20, p̂2 = .30 d. n1 = 100, n2 =
Independent random samples, each containing 800 observations, were selected from two binomial populations. The samples from populations 1 and 2 produced 320 and 400 successes, respectively.a. Test H0: (p1 - p2) = 0 against Ha: (p1 - p2) = 0. Use α ≠ .05.b. Test H0: (p1 - p2) = 0 against Ha: (p1
Sketch the sampling distribution of (p̂1 - p̂2) based on independent random samples of n1 = 100 and n2 = 200 observations from two binomial populations with probabilities of success p1 = .1 and p2 = .5, respectively.
July is National Grilling Month in the United States. On July 1, 2008, The Harris Poll #70 reported on a survey of Americans’ grilling preferences. When asked about their favorite food prepared on a barbeque grill, 662 of 1,250 randomly sampled Democrats preferred steak, as compared to 586 of 930
American Demographics (Jan. 2002) reported the results of a survey on the planning habits of men and women. In response to the question “What is your preferred method of planning and keeping track of meetings, appointments, and deadlines?” 56% of the men and 46% of the women answered “I keep
Angioplasty’s benefits challenged. Each year, more than 1 million heart patients undergo an angioplasty. The benefits of an angioplasty were challenged in a recent study of 2,287 patients (2007 Annual Conference of the American College of Cardiology, New Orleans). All the patients had substantial
Effectiveness of drug tests of Olympic athletes. Erythropoietin (EPO) is a banned drug used by athletes to increase the oxygen-carrying capacity of their blood. New tests for EPO were first introduced prior to the 2000 Olympic Games held in Sydney, Australia. Chance (Spring 2004) reported that of a
Detection of rigged school milk prices (cont€™d). Refer to the investigation of collusive bidding in the northern Kentucky school milk market, presented in Exercise. Market allocation is a common form of collusive behavior in bid-rigging conspiracies. Under collusion, the same dairy
Gonzaga University professors conducted a study of television commercials and published their results in the Journal of Sociology, Social Work and Social Welfare (Vol. 2, 2008). The key research question was: “Do television advertisers use religious symbolism to sell goods and services?” In a
If the sample-size calculation yields a value of n that is too large to be practical, how should you proceed?
Find the appropriate values of n1 and n2 (assume that n1 = n2) needed to estimate (µ1 - µ2) with a. A sampling error equal to 3.2 with 95% confidence. From prior experience, it is known that σ1 ≈ 15 and σ2 ≈ 17. b. A sampling error equal to 8 with 99% confidence. The range of each
Enough money has been budgeted to collect independent random samples of size n1 = n2 = 100 from populations 1 and 2 in order to estimate (p1 – p2). Prior information indicates that p1 = p2 = .6. Have sufficient funds been allocated to construct a 90% confidence interval for (p1 - p2) of width .1
Refer to the Journal of Deaf Studies and Deaf Education (Fall 2006) paired difference study on vocalized laughter among deaf users of sign language, presented in Exercise. Suppose you want to estimate µd = (µS - µA), the difference between the population mean number of laugh episodes of deaf
All cable television companies carry at least one home-shopping channel. Who uses these home-shopping services? Are the shoppers primarily men or women? Suppose you want to estimate the difference in the percentages of men and women who say they have used or expect to use televised home shopping.
Poisons are used to prevent rat damage in sugarcane fields. The U.S. Department of Agriculture is investigating whether the rat poison should be located in the middle of the field or on the outer perimeter. One way to answer this question is to determine where the greater amount of damage occurs.
The F-statistic used for testing H0: σ12 = σ22 against Ha: σ12 < σ22 is F = (s1)2/(s2)2.
Use Tables VIII, IX, X, and XI of Appendix A to find each of the following F -values: a. F.05, where v1 = 8 and v2 = 5 b. F.01, where v1 = 20 and v2 = 14 c. F.025, where v1 = 10 and v2 = 5 d. F.10, where v1 = 20 and v2 = 5
For each of the cases that follow, identify the rejection region that should be used to test H0: σ12 = σ22 against Ha: σ12 > σ22. Assume that n1 = 20 and n2 = 30. a. α = .10 b. α = .05 c. α = .025 d. α = .01
Specify the appropriate rejection region for testing against H0: Ïƒ12 = Ïƒ22 in each of the following situations:
A quasar is a distant celestial object (at least 4 billion light-years away) that provides a powerful source of radio energy. The Astronomical Journal (July 1995) reported on a study of 90 quasars detected by a deep-space survey. The survey enabled astronomers to measure several different
Refer to Exercise 9.19. The €œfear of negative evaluation€ (FNE) scores for the 11 bulimic females and 14 females with normal eating habits are reproduced in the table below and saved in the BULIMIA file. The confidence interval you constructed in Exercise 9.19 requires that
Refer to the Journal of Biogeography (Dec. 2003) study of ants in Mongolia (central Asia), presented in Exercise, in which you compared the mean number of ants at two desert sites. Since the sample sizes were small, the variances of the populations at the two sites must be equal in order for the
Patent infringement case. Refer to the Chance (Fall2002) description of a patent infringement case against Intel Corp., presented in Exercise. The zinc measurements for three locations listed in the original inventor€™s notebook€”on a text line, on a witness line, and on the intersection of
Detection of rigged school milk prices (cont€™d). Refer to the investigation into collusive bidding in the northern Kentucky school milk market, presented in Exercises. In competitive sealed-bid markets, vendors do not share information about their bids. Consequently, more dispersion or
List the assumptions necessary for each of the following inferential techniques: a. Large-sample inferences about the difference (µ1 – µ2) between population means, using a two-sample z–statistic b. Small-sample inferences about (µ1 – µ2), using an independent samples design and a
Two independent random samples were selected from normally distributed populations with means and variances (µ1, σ21) and (µ2, σ22), respectively. The sample sizes, means, and variances are shown in the following table: Sample 1 ... Sample 2 n1 = 20 ..... n2 = 15 x̄1 = 123 ....
Independent random samples were selected from two binomial populations. The size and number of observed successes for each sample are shown in the following table:Sample 1Sample 2n1 = 200 .....n2 = 200x̄1 = 110 ......x̄2 = 130a. Test H0: (p1 - p2) = 0 against Ha: (p1 - p2) < 0. Use α = .10.b.
A random sample of five pairs of observations was selected, one observation from a population with mean µ1, the other from a population with mean µ2. The data are shown in the following table and saved in the LM9_112 file.a. Test the null hypothesis H0: µd = 0 against Ha: µd = 0, where µd =
A study published in the Journal of American Academy of Business, Cambridge (March 2002) examined whether the perception of the quality of service at five-star hotels in Jamaica differed by gender. Hotel guests were randomly selected from the lobby and restaurant areas and asked to rate 10
Refer to the Journal of Sport Behavior (2001) study of variety in exercise workouts, presented in Exercise. One group of 40 people varied their exercise routine in workouts, while a second group of 40 exercisers had no set schedule or regulations for their workouts. By the end of the study, 15
Pig bile study. Bear gallbladder is used in Chinese medicine to treat inflammation. A study in the Journal of Ethnopharmacology (June 1995) examined the easier-to-obtain pig gallbladder as an effective substitute for bear gallbladder. Twenty male mice were divided randomly into two groups: Ten were
Some power plants are located near rivers or oceans so that the available water can be used to cool the condensers. Suppose that, as part of an environmental impact study, a power company wants to estimate the difference in mean water temperature between the discharge of its plant and the offshore
Does winning an Academy of Motion Picture Arts and Sciences award lead to long-term mortality for movie actors? In an article in the Annals of Internal Medicine (May 15, 2001), researchers sampled 762 Academy Award winners and matched each one with another actor of the same sex who was in the same
Hermaphrodites are animals that possess the reproductive organs of both sexes. Genetical Research (June 1995) published a study of the mating systems of hermaphroditic snail species. The mating habits of the snails were classified into two groups:(1) Self-fertilizing (selfing) snails that mate with
Identical twins reared apart. Because they share an identical genotype, twins make ideal subjects for investigating the degree to which various environmental conditions affect personality. The classical method of studying this phenomenon, nomenon, and the subject of an interesting book by Susan
Do cocaine abusers have radically different personalities than non-abusing college students? This was one of the questions researched in Psychological Assessment (June 1995). Zuckerman€“Kuhlman€™s Personality Questionnaire (ZKPQ) was administered to a sample of 450 cocaine abusers and a
Swim maze study. Merck Research Labs used the single-T swim maze to conduct an experiment to evaluate the effect of a new drug. Nineteen impregnated dam rats were allocated a dosage of 12.5 milligrams of the drug. One male and one female rat pup were randomly selected from each resulting litter to
For each of the following studies, give the parameter of interest and state any assumptions that are necessary for the inferences to be invalid. a. To investigate a possible link between jet lag and memory impairment, a University of Bristol (England) neurologist recruited 20 female flight
Japanese researchers have developed a compression€“depression method of testing electronic circuits based on Huffman coding (IEICE Transactions on Information & Systems, Jan. 2005). The new method is designed to reduce the time required for input decompression and output
To help students organize global information about people, places, and environments, geographers encourage them to develop “mental maps” of the world. A series of lessons was designed to aid students in the development of mental maps (Journal of Geography, May/June 1997). In one experiment, a
The Florida Scientist (Summer/Autumn 1991) reported on a study of the feeding habits of sea urchins. A sample of 20 urchins was captured from Biscayne Bay (Miami), placed in marine aquaria, and then starved for 48 hours. Each sea urchin was then fed a 5-cm blade of turtle grass. Ten of the urchins
MS and exercise study. A study published in Clinical Kinesiology (Spring 1995) was designed to examine the metabolic and cardiopulmonary responses during exercise of persons diagnosed with multiple sclerosis (MS).Leg-cycling and arm-cranking exercises were performed by 10 MS patients and 10 healthy
To use the t-statistic to test for a difference between the means of two populations, what assumptions must be made about the two populations? About the two samples?
A confidence interval for (µ1 - µ2) is (-10, 4). Which of the following inferences is correct?a. µ1 > µ2b. µ1 < µ2c. µ1 = µ2d. no significant difference between means
In order to compare the means of two populations, independent random samples of 400 observations are selected from each population, with the following results:Sample 1 Sample 2x̄1 = 5,275 .... x̄2 = 5,240s1 = 150 ...... s2 = 200a. Use a 95% confidence interval to estimate the difference between
Assume that σ12 = σ22 = σ2. Calculate the pooled estimator of σ2 for each of the following cases: a. s12 = 200, s22 = 180, n1 = n2 = 25 b. s12 = 25, s22 = 40, n1 = 20, n2 = 10 c. s12 = .20, s22 = .30, n1 = 8, n2 = 12 d. s12 = 2,500, s22 = 1,800, n1 = 16, n2 = 17 e. Note that the pooled estimate
Two independent random samples have been selected, 100 observations from population 1 and 100 from population 2. Sample means x̄1 = 70 and x̄2 = 50 were obtained. From previous experience with these populations, it is known that the variances are σ12 = 100 and σ22 = 64.a. Find σ(x̄1 -
Independent random samples selected from two normal populations produced the following sample means and standard deviations:Sample 1 ....Sample 2n1 = 17 ...... n2 = 12x̄1 = 5.4 ......x̄2 = 7.9s1 = 3.4 .....s2 = 4.8a. Assuming equal variances, conduct the test H0: (µ1 - µ2) = 0 against Ha: (µ1
A study of the differences in cognitive function between normal individuals and patients diagnosed with schizophrenia was published in the American Journal of Psychiatry (April 2010). The total time (in minutes) a subject spent on the Trail Making Test (a standard psychological test) was used as a
The Ohio Environmental Protection Agency used the Index of Biotic Integrity (IBI) to measure the biological condition, or €œhealth,€ of an aquatic region. The IBI is the sum of metrics that measure the presence, abundance, and health of fish in the region.Researchers collected IBI
Refer to the Bulletin of Marine Science (April 2010) study of lobster trap placement, Exercise. Recall that the variable of interest was the average distance separating traps€”called trap spacing €”deployed by teams of fishermen fishing for the red spiny lobster in Baja California Sur,

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