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Questions and Answers of Statistics

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
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
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
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 =
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
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
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
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
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
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
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
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 >
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
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
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
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
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
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,
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
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
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
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
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
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
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,
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
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
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
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
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
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.
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.
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 =
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
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).
"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
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
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.
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
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
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
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
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 ,
"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
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.
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
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
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
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
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
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
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
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
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
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.
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
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
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
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,
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 =
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
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
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
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
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
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
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
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 =
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
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.
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
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
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
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
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
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
Do cocaine abusers have radically different personalities than non-abusing college students? This was one of the questions researched in Psychological Assessment (June 1995).
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
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
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
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
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
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
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
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 =
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
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 =
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
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
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

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