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A First Course In Statistics 12th Edition James T McClave, Terry T Sincich - Solutions

Characteristics of antiwar demonstrators. Refer to the American Journal of Sociology (Jan. 2014) study of the characteristics of antiwar demonstrators in the United States, Exercise 2.106 (p. 101). The researchers found that the mean number of protest organizations joined by antiwar demonstrators
Critical part failures in NASCAR vehicles. The Sport Journal (Winter 2007) published a study of critical part failures at NASCAR races. The researchers found that the time x (in hours) until the first critical part failure has a skewed distribution with m = .10 and s = .10. Now, consider a random
Motivation of drug dealers. Refer to the Applied Psychology in Criminal Justice (Sept. 2009) investigation of the personality characteristics of drug dealers, Exercise 2.102 (p. 101). Convicted drug dealers were scored on the Wanting Recognition (WR) Scale—a scale that provides a quantitative
Tomato as a taste modifier. Miraculin is a protein naturally produced in a rare tropical fruit that can convert a sour taste into a sweet taste. Refer to the Plant Science(May 2010) investigation of the ability of a hybrid tomato plant to produce miraculin, Exercise 5.38 (p. 296). Recall that the
Shell lengths of sea turtles. Refer to the Aquatic Biology(Vol. 9, 2010) study of green sea turtles inhabiting the Grand Cayman South Sound lagoon, Exercise 2.85 (p. 93).Research shows that the curved carapace (shell) lengths of these turtles has a distribution with mean m = 50 cm and standard
Requests to a Web server. Brighton Webs LTD modeled the arrival time of requests to a Web server within each hour using a uniform distribution (see Example 4.27). Specifically, the number of seconds x from the start of the hour that the request is made is uniformly distributed between 0 and 3,600
Phishing attacks to e-mail accounts. In Exercise 2.47(p. 77), you learned that phishing describes an attempt to extract personal/financial information from unsuspecting people through fraudulent e-mail. Data from an actual phishing attack against an organization were presented in Chance (Summer
Voltage sags and swells. Refer to the Electrical Engineering(Vol. 95, 2013) study of the power quality (sags and swells)of a transformer, Exercise 2.127 (p. 106). For transformers built for heavy industry, the distribution of the number of sags per week has a mean of 353 with a standard deviation
Corporate sustainability of CPA firms. Refer to the Business and Society (Mar. 2011) study on the sustainability behaviors of CPA corporations, Exercise 1.26 (p. 46).Recall that corporate sustainability refers to business practices designed around social and environmental considerations.The level
4.8 Open the applet entitled Sampling Distributions. On the pulldown menu to the right of the top graph, select Uniform. The box to the left of the top graph displays the population mean, median, and standard deviation of the original distribution.a. Run the applet for the sample size n = 30 and
A random sample of n = 100 observations is selected from a population with m = 31 and s = 25.a. Find mx and sx.b. Describe the shape of the sampling distribution of x.c. Find P1x Ú 282.d. Find P122.1 … x … 26.82.e. Find P1x … 28.22.f. Find P1x Ú 27.02.Applet Exercise 4.7 Open the applet
Consider the following probability distribution:x 3 4 6 9 p1x2 .3 .1 .5 .1a. Find m, s2, and s.b. Find the sampling distribution of x for random samples of n = 2 measurements from this distribution by listing all possible values of x, and find the probability associated with each.c. Use the results
Suppose a random sample of n = 16 measurements is selected from a population with mean m and standard deviation s. For each of the following values of m and s, give the values of mx and sx.a. m = 12, s = 3b. m = 144, s = 16c. m = 24, s = 28d. m = 12, s = 96
Suppose a random sample of n measurements is selected from a population with mean m = 225 and variance s2 = 225. For each of the following values of n, give the mean and standard deviation of the sampling distribution of the sample mean x.a. n = 9b. n = 49c. n = 225d. n = 500e. n = 1,000f. n = 2,500
Will the sampling distribution of x always be approximately normally distributed? Explain.Learning the Mechanics
In Example 4.27, we used the computer to generate 1,000 samples, each containing n = 11 observations, from a uniform distribution over the interval from 150 to 200. Now use the computer to generate 500 samples, each containing n = 15 observations, from that same population.a. Calculate the sample
Refer to Exercise 4.147. Assume that a random sample of n = 2 measurements is randomly selected from the population.a. List the different values that the sample median M may assume, and find the probability of each. Then give the sampling distribution of the sample median.b. Construct a probability
Refer to Exercise 4.147 and find E1x2 = m. Then use the sampling distribution of x found in Exercise 4.147 to find the expected value of x. Note that E1x2 = m.
Consider the population described by the probability distribution shown below. The random variable x is observed twice with independent observations.x 0 1 2 3 p1x2 0.3 0.2 0.3 0.2 The random variable x is observed twice. If these observations are independent, verify that the different samples of
Simulate sampling from the population described in Exercise 4.145 by marking the values of x, one on each of four identical coins (or poker chips, etc.). Place the coins(marked 0, 2, 4, and 6) into a bag, randomly select one, and observe its value. Replace this coin, draw a second coin, and observe
What is a sampling distribution of a sample statistic?Learning the Mechanics
Marital name changing. Refer to the Advances in Applied Sociology (Nov. 2013) study of marital name changing, Exercise 4.66 (p. 217). Recall that the probability that an American female will change her last name upon marriage is .9. In a sample of 500 European females, suppose researchers find that
Fingerprint expertise. Refer to the Psychological Science(Aug. 2011) study of fingerprint identification, Exercise 4.63 (p. 217). Recall that the study found that when presented with prints from the same individual, a novice will correctly identify the match only 75% of the time. Now consider a
Chemical signals of mice. Refer to the Cell (May 14, 2010)study of the ability of a mouse to recognize the odor of a potential predator, Exercise 4.61 (p. 217). You learned that 40% of lab mice cells exposed to chemically produced major urinary proteins (Mups) from a cat responded positively(i.e.,
LASIK surgery complications. According to studies, 1%of all patients who undergo laser surgery (i.e., LASIK) to correct their vision have serious post-laser vision problems(All About Vision, 2014). In a random sample of 200,000 LASIK patients, let x be the number who experience serious post-laser
Cesarean birth study. In Exercise 4.62 (p. 217), you learned that 32% of all births in the United States occur by Cesarean section each year (National Vital Statistics Reports, Mar.2010). In a random sample of 1,000 births this year, let x be the number that occur by Cesarean section.a. Find the
Where will you get your next pet? Refer to Exercise 4.60(p. 217) and the associated poll that revealed that half of all pet owners would get their next dog or cat from a shelter. Consider a random sample of 700 pet owners and define x as the number of pet owners who would acquire their next dog or
Working on summer vacation. In Exercise 4.58, (p. 216), you learned that 30% of adults do not work at all while on summer vacation. Now consider a random sample of 1,500 adults and let x represent the number who do not work during summer vacation.a. What is the expected value of x? Interpret this
Blood diamonds. According to Global Research News(Mar. 4, 2014), one-fourth of all rough diamonds produced in the world are blood diamonds, i.e., diamonds mined to finance war or an insurgency. In a random sample of 1,000 rough diamonds purchased by a diamond buyer, let x be the number that are
Assume that x is a binomial random variable with n = 120 and p = .50. Use a normal approximation to find the following:a. P1x … 552b. P160 … x … 802c. P1x Ú 582 Applying the Concepts—Basic
Assume that x is a binomial random variable with n = 1,200 and p = .50. Find each of the following probabilities:a. n = 80, p = 0.03b. n = 100, p = 0.04a. P1x 7 6002b. P1589 … x 6 6002c. P1x 7 6552
Assume that x is a binomial random variable with n = 20 and p = .5. Use Table I of Appendix B and the normal approximation to find the exact and approximate values, respectively, of the following probabilities:a. P1x … 92b. P1x Ú 112c. P18 … x … 112
Assume that x is a binomial random variable with n and p as specified in parts a–f that follow. For which cases would it be appropriate to use a normal distribution to approximate the binomial distribution?a. n = 80, p = 0.03b. n = 100, p = 0.04c. n = 10, p = 0.6d. n = 500, p = .05e. n = 200, p =
Can a binomial distribution with parameters n = 10 and p = .1 be well approximated by a normal distribution?Learning the Mechanics
Ranking Ph.D. programs in economics. Refer to the Southern Economic Journal (Apr. 2008) rankings of Ph.D. programs in economics at 129 colleges and universities, Exercise 2.129 (p. 107). Recall that the number of publications published by faculty teaching in the Ph.D.program and the quality of the
Blond hair types in the Southwest Pacific. Refer to the American Journal of Physical Anthropology (Apr. 2014)study of a mutation of blond-hair genotypes, Exercise 2.141(p. 115). Recall that for each of 550 Southwest Pacific islanders, the effect of the mutation on hair pigmentation was measured
Cruise ship sanitation scores. Refer to the data on the Aug.2013 sanitation scores for 186 cruise ships, presented in Exercise 2.41 (p. 75). The data are saved in the SANIT file.Assess whether the sanitation scores are approximately normally distributed.Applying the Concepts—Advanced
Permeability of sandstone during weathering. Refer to the Geographical Analysis (Vol. 42, 2010) study of the decay properties of sandstone when exposed to the weather, Exercise 2.69 (p. 87). Recall that blocks of sandstone were cut into 300 equal-sized slices and the slices randomly divided into
Ranking the driving performance of professional golfers.Refer to The Sport Journal (Winter 2007) article on a new method for ranking the driving performance of PGA golfers, presented in Exercise 2.66 (p. 86). Recall that the method incorporates a golfer’s average driving distance(yards) and
Mineral flotation in water study. Refer to the Minerals Engineering (Vol. 46–47, 2013) study of the impact of calcium and gypsum on the flotation properties of silica in water, Exercise 2.48 (p. 77). Recall that 50 solutions of deionized water were prepared both with and without calcium/gypsum,
Drug content assessment. Scientists at GlaxoSmithKline Medicines Research Center used high-performance liquid chromatography (HPLC) to determine the amount of drug in a tablet produced by the company (Analytical Chemistry, Dec. 15, 2009). Drug concentrations (measured as a percentage) for 50
Estimating glacier elevations. Digital elevation models(DEMs) are now used to estimate elevations and slopes of remote regions. In Arctic, Antarctic, and Alpine Research(May 2004), geographers analyzed reading errors from maps produced by DEMs. Two readers of a DEM map of White Glacier (in Canada)
Shear strength of rock fractures. Understanding the characteristics of rock masses, especially the nature of the fractures, are essential when building dams and power plants.The shear strength of rock fractures was investigated in Engineering Geology (May 12, 2010). The Joint Roughness Coefficient
Characteristics of antiwar demonstrators. Refer to the American Journal of Sociology (Jan. 2014) study of the characteristics of antiwar demonstrators in the United States, Exercise 2.106 (p. 101). Based on data collected for over 5,000 antiwar demonstrators over a recent 3-year period, the
Irrelevant speech effects. Refer to the analysis of irrelevant speech effects in Exercise 2.34 (p. 73). Recall that irrelevant speech effects refer to the degree to which the memorization process is impaired by irrelevant background speech. In a study published in Acoustical Science& Technology
Examine the sample data in the next column.L04110a. Construct a stem-and-leaf plot to assess whether the data are from an approximately normal distribution.b. Compute s for the sample data.5.9 5.3 1.6 7.4 8.6 3.2 2.1 4.0 7.3 8.4 5.9 6.7 4.5 6.3 6.0 9.7 3.5 3.1 4.3 3.3 8.4 4.6 8.2 6.5 1.1 5.0 9.4
Examine the following sample data.32 48 25 135 53 37 5 39 213 165 109 40 1 146 39 25 21 66 64 57 197 60 112 10 155 134 301 304 107 82 35 81 60 95 401 308 180 3 200 59a. Construct a stem-and-leaf plot to assess whether the data are from an approximately normal distribution.b. Find the values of QL,
How do you use IQR to check that the data came from a standard normal distribution?Learning the Mechanics
Alcohol, threats, and electric shocks. A group of Florida State University psychologists examined the effects of alcohol on the reactions of people to a threat (Journal of Abnormal Psychology, Vol. 107, 1998). After obtaining a specified blood alcohol level, the psychologists placed experimental
Safety of underground tunnels. Research published in the journal Tunnelling and Underground Space Technology(July 2014) evaluated the safety of underground tunnels built in rigid soils. A Factor of Safety (FS), measured as the ratio of capacity over demand, was determined for three different areas
Voltage sags and swells. Refer to the Electrical Engineering(Vol. 95, 2013) study of the power quality of a transformer, Exercise 2.127 (p. 106). Recall that two causes of poor power quality are “sags” and “swells.” (A sag is an unusual dip and a swell is an unusual increase in the voltage
Flicker in an electrical power system. An assessment of the quality of the electrical power system in Turkey was the topic of an article published in Electrical Engineering(Mar. 2013). One measure of quality is the degree to which voltage fluctuations cause light flicker in the system.The
Shell lengths of sea turtles. Refer to the Aquatic Biology (Vol.9, 2010) study of green sea turtles inhabiting the Grand Cayman South Sound lagoon, Exercise 2.85 (p. 93). Researchers discovered that the curved carapace (shell) length of these turtles is approximately normally distributed with mean
Shopping vehicle and judgment. Refer to the Journal of Marketing Research (Dec. 2011) study of whether you are more likely to choose a vice product (e.g., a candy bar)when your arm is flexed (as when carrying a shopping basket)than when your arm is extended (as when pushing a shopping cart),
4.6 Open the applet entitled Sample from a Population. On the pulldown menu to the right of the top graph, select Bell shaped. The box to the left of the top graph displays the population mean, median, and standard deviation.a. Run the applet for each available value of n on the pulldown menu for
The random variable x has a normal distribution with standard deviation 20. It is known that the probability that x exceeds 150 is 0.90. Find the mean m of the probability distribution.
Suppose x is a normally distributed random variable with m = 30 and s = 8. Find a value x0 of the random variable x such thata. P1x Ú x02 = .5b. P1x 6 x02 = .025c. P1x 7 x02 = .10d. P1x 7 x02 = .95e. 10% of the values of x are less than x0.f. 80% of the values of x are less than x0.g. 1% of the
Find a value z0 of the standard normal random variable z such thata. P1z Ú z02 = .05b. P1z Ú z02 = .025c. P1z … z02 = .025d. P1z Ú z02 = .10e. P1z 7 z02 = .10
Find a value z0 of the standard normal random variable z such thata. P1z Ú z02 = 0.10b. P1z Ú z02 = 0.03c. P1z … z02 = 0.01d. P1z Ú z02 = 0.20e. P1z 7 z02 = 0.02f. P1 -2.33 6 z 6 1.502 g. P1z Ú -2.332 h. P1z 6 2.332
Give the z-score for a measurement from a normal distribution for the following:a. 2 standard deviation above the meanb. 2 standard deviation below the meanc. Equal to the meand. 2.5 standard deviations above the meane. 3 standard deviations above the meanf. P1 -2 … z … 22 g. P1 -2.16 … z …
Find the area under the standard normal probability distribution between the following pairs of z-scores:a. z = 0 and z = 1.90b. z = 0 and z = 0.90c. z = 0 and z = 2.90d. z = 0 and z = 0.e. z = -1.90 and z = 0f. z = -0.90 and z = 0 g. z = -1.59 and z = 0 h. z = -0.48 and z = 0
What is the name given to a normal distribution when m = 0 and s = 1?Learning the Mechanics
Assigning a passing grade. A literature professor decides to give a 25-question true–false quiz to determine who has read an assigned novel. She wants to choose the passing grade such that the probability of passing a student who guesses on every question is less than 0.1. What score should she
Testing a psychic’s ESP. Refer to Exercise 3.101 (p. 180)and the experiment conducted by the Tampa Bay Skeptics to see whether an acclaimed psychic has extrasensory perception (ESP). Recall that a crystal was placed, at random, inside 1 of 10 identical boxes lying side by side on a table. The
Fingerprint expertise. Psychological Science (Aug. 2011)published a study of fingerprint identification. The study found that when presented with prints from the same individual, a fingerprint expert will correctly identify the match 92% of the time. In contrast, a novice will correctly identify
Caesarian births. A medical research reports that 75% of all births in a certain region take place by Caesarian section each year.a. In a random sample of 1,000 births, how many, on average, will take place by Caesarian section?b. What is the standard deviation of the number of Caesarian section
Chemical signals of mice. Refer to the Cell (May 14, 2010)study of the ability of a mouse to recognize the odor of a potential predator, Exercise 3.63 (p. 165). Recall that the sources of these odors are typically major urinary proteins(Mups). In an experiment, 40% of lab mice cells exposed to
Where will you get your next pet? According to an Associated Press/Petside.com poll, half of all pet owners would get their next dog or cat from a shelter (USA Today, May 12, 2010). Consider a random sample of 20 pet owners and define x as the number of pet owners who would acquire their next dog
4.5 Use the applet entitled Simulating the Stock Market to estimate the probability that the stock market will go up each of the next two days. Repeatedly run the applet for n = 2, recording the number of ups each time. Use the proportion of 2’s among your results as the estimate of the
4.4 Open the applet entitled Sample from a Population. On the pull-down menu to the right of the top graph, select Binary. Set n = 10 as the sample size and repeatedly choose samples from the population. For each sample, record the number of 1’s in the sample. Let x be the number of l’s in a
The binomial probability distribution is a family of probability distributions with each single distribution depending on the values of n and p. Assume that x is a binomial random variable with n = 10.a. Determine a value of p such that the probability distribution of x is symmetric.b. Determine a
If x is a binomial random variable, use Table I in Appendix B or technology to find the following probabilities:a. P1x = 22 for n = 10, p = .4b. P1x … 52 for n = 15, p = .6c. P1x 7 12 for n = 5, p = .1
If x is a binomial random variable, compute p1x2 for each of the following cases:a. n = 5, x = 1, p = .2b. n = 4, x = 2, q = .4c. n = 3, x = 0, p = .7d. n = 5, x = 3, p = .1e. n = 4, x = 2, q = .6f. n = 3, x = 1, p = .9
Compute the following:a.5!2!15 - 22!d. a 7 7 be. a 5 3 bb. a 6 2 bc. a 5 0 b
Consider the following binomial probability distribution:p1x2 = a 7x b 1.42x1.627 - x 1x = 0, 1, 2,c, 72a. How many trials (n) are in the experiment?b. What is the value of p, the probability of success?
Give the formula for p1x2 for a binomial random variable with n = 7 and p = .2.
Punnett square for earlobes. Geneticists use a grid—called a Punnett square—to display all possible gene combinations in genetic crosses. (The grid is named for Reginald Punnett, a British geneticist who developed the method in the early 1900s.) The figure below is a Punnett square for a cross
Voter preferences for a committee. A “Condorcet”committee of, say, 3 members is a committee that is preferred by voters over any other committee of 3 members.A scoring function was used to determine “Condorcet”committees in Mathematical Social Sciences (Nov. 2013).Consider a committee with
Expected winnings in roulette. In the popular casino game of roulette, you can bet on whether the ball will fall in an arc on the wheel colored red, black, or green. You showed(Exercise 3.127, p. 185) that the probability of a red outcome is 18/38, that of a black outcome is 18/38, and that of a
Beach erosional hot spots. Refer to the U.S. Army Corps of Engineers’ study of beach erosional hot spots, presented in Exercise 3.123 (p. 184). The data on the nearshore bar condition for six beach hot spots are reproduced in the accompanying table. Suppose you randomly select two of these six
Reliability of a manufacturing network. A team of industrial management university professors investigated the reliability of a manufacturing system that involves multiple production lines (Journal of Systems Sciences & Systems Engineering, Mar. 2013). An example of such a network is a system for
Choosing portable grill displays. Refer to the Journal of Consumer Research (Mar. 2003) marketing study of influencing consumer choices by offering undesirable alternatives, presented in Exercise 3.29 (p. 153). Recall that each of 124 college students selected showroom displays for portable grills.
Environmental vulnerability of amphibians. Many species of amphibians are declining due to dramatic changes in the environment. The environmental vulnerability of amphibian species native to Mexico was examined in Amphibian& Reptile Conservation (Aug. 2013). The researchers quantified this decline
Gender in two-child families. Human Biology (Feb. 2009)published a study on the gender of children in two-child families. In populations where it is just as likely to have a boy as a girl, the probabilities of having two girls, two boys, or a boy and a girl are well known. Let x represent the
Controlling the water hyacinth. An insect that naturally feeds on the water hyacinth, one of the world’s worst aquatic weeds, is the delphacid. Female delphacids lay anywhere from one to four eggs onto a water hyacinth blade. The Annals of the Entomological Society of America(Jan. 2005) published
NHTSA crash tests. Refer to the National Highway Traffic Safety Administration (NHTSA) crash tests of new car models, presented in Exercise 4.6 (p. 194). A summary of the driver-side star ratings for the 69 cars is reproduced in the MINITAB printout in the next column. Assume that 1 of the 69 cars
Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, Exercise 2.7(p. 62). Recall that in a random sample of 106 social (or service) robots designed to entertain, educate, and care for human
4.2 Run the applet entitled Simulating the Probability of a Head with a Fair Coin 10 times with n = 2, resetting between runs, to simulate flipping two coins 10 times. Count and record the number of heads each time. Let x represent the number of heads on a single flip of the coins.a. What are the
4.1 Use the applet entitled Random Numbers to generate a list of 25 numbers between 1 and 3, inclusive. Let x represent a number chosen from this list.a. What are the possible values of x?b. Give the probability distribution for x in table form.c. Let y be a number randomly chosen from the set 51,
Consider the probability distributions shown here:x 3 4 5 p(x) .3 .4 .3 y 3 4 5 p(y) .1 .8 .1a. Use your intuition to find the mean for each distribution.How did you arrive at your choice?b. Which distribution appears to be more variable? Why?c. Calculate m and s2 for each distribution. Compare
Consider the probability distribution shown here:x -4 -3 -2 -1 0 1 2 3 4 p(x) .02 .07 .10 .15 .30 .18 .10 .06 .02a. Calculate m, s2, and s.b. Graph p1x2. Locate m, m - 2s, and m + 2s on the graph.c. What is the probability that x will fall into the interval m { 2s?
Consider the probability distribution for the random variable x shown here:x -1 1 2 5 y .2 .4 .2 .2a. Find m = E1x2.b. Find s2 = E31x - m224.c. Find s.d. Interpret the value you obtained for m.e. In this case, can the random variable x ever assume the value m? Explain.f. In general, can a random
The random variable x has the following discrete probabil-ity distribution:x 56 78 9p(x).2.3.2.1.2 Since the values that x can assume are mutually exclusive events, the event { x = 7} is the union of three mutually exclusive events:{x = 5} U {x = 6} U {x = 7}a. Find P(x ≤ 7).b. Find P(x > 7).c.
Explain why each of the following is or is not a valid prob-ability distribution for a discrete random variable x:a.x 01 33 p(x).2.3 2b. x-2-1 0p(x).25.50.20c. x 49 20 p(x)-. 3 1.0.3d. x 23 56 p(x)15.20,40.35
A discrete random variable x can assume five possible values: 20, 21, 22, 23, and 24. The MINITAB histogram at the next page shows the likelihood of each value.a. What is p(22)?b. What is the probability that x equals 20 or 24?c. What is P1x … 232?
For a mound-shaped, symmetric distribution, what is the probability that x falls into the interval m { 3s?
How do you represent the probability distribution of a random variable denoting the number of heads when an unbiased coin tossed once?Learning the Mechanics
Shaft graves in ancient Greece. Refer to the American Journal of Archaeology (Jan. 2014) study of shaft graves in ancient Greece, Exercise 2.37 (p. 74). Let x represent the number of decorated sword shafts buried at a discovered grave site. Explain why x is a discrete random variable.
Irrelevant speech effects. Refer to the Acoustical Science& Technology (Vol. 35, 2014) study of the degree to which the memorization process is impaired by irrelevant background speech (called irrelevant speech effects), Exercise 2.34 (p. 73). Recall that subjects performed a memorization task
Motivation of drug dealers. Refer to the Applied Psychology in Criminal Justice (Sept. 2009) study of the personality characteristics of drug dealers, Exercise 2.102(p. 101). For each of 100 convicted drug dealers, the researchers measured several variables, including the number of prior felony

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