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Statistics 13th Global Edition James T. McClave And Terry T Sincich - Solutions
Find the numerical values of LO5a. a6 3 bb. P52c. P42d. a100 98 be. a50 50 bf. a50 0 b g. P53 h. P10
Determine the number of sample points contained in the sample space when you toss the following: LO5a. 1 dieb. 2 dicec. 4 diced. n dice
Cheek teeth of extinct primates. Refer to the American Journal of Physical Anthropology (Vol. 142, 2010) study of the dietary habits of extinct mammals, Exercise 3.25(p. 158). Recall that 18 cheek teeth extracted from skulls of an extinct primate species discovered in western Wyoming were analyzed.
Randomization in a study of TV commercials. Gonzaga University professors conducted a study of over 1,500 television commercials and published their results in the Journal of Sociology, Social Work and Social Welfare (Vol.2, 2008). Commercials from eight networks—ABC, FAM, FOX, MTV, ESPN, CBS,
A straight flush in poker. Consider 5-card poker hands dealt from a standard 52-card bridge deck. Two important events are A: 5You draw a flush.6 B: 5You draw a straight.6[Note: A flush consists of any 5 cards of the same suit. A straight consists of any 5 cards with values in sequence. In a
An unmanned monitoring system uses high-tech video equipment and microprocessors to detect intruders. A prototype system has been developed and is in use outdoors at a weapons munitions plant. The system is designed to detect intruders with a probability of .90. However, the design engineers expect
Electric wheelchairs are difficult to maneuver for many disabled people. In a paper presented at the 1st International Workshop on Advances in Service Robotics (Mar.2003), researchers applied Bayes’s rule to evaluate an “intelligent” robotic controller that aims to capture the intent of a
Explain the difference between the two probabilities P1A0B2 and P1B0A2. LO5
Why is Bayes’s rule unnecessary for finding P1B0A2 if LO5 events A and B are independent?
Why is Bayes’s rule unnecessary for finding P1B0A2 if events A and B are mutually exclusive? LO5
Fingerprint expertise. A study published in Psychological Science (Aug. 2011) tested the accuracy of experts and novices in identifying fingerprints. Participants were presented pairs of fingerprints and asked to judge whether the prints in each pair matched. The pairs were presented under three
Tests for Down syndrome. Currently, there are three diagnostic tests available for chromosome abnormalities in a developing fetus: triple serum marker screening, ultrasound, and amniocentesis. The safest (to both the mother and fetus) and least expensive of the three is the ultrasound test. Two San
Which of the following pairs of events are mutually exclusive?a. A = 5The Tampa Bay Rays win the World Series next year.6 B = 5Evan Longoria, Rays infielder, hits 75 home runs runs next year.6b. A = 5Psychiatric patient Tony responds to a stimulus within 5 seconds.6 B = 5Psychiatric patient Tony
A sample space consists of four sample points S1, S2, S3, and S4, where P1S12 = .3, P1S22 = .3, P1S32 = .2, and P1S42 = .2.a. Show that the sample points obey the two probability LO5 rules for a sample space.b. If an event A = 5S1, S46, find P(A).
A and B are mutually exclusive events, with P1A2 = .3 and P1B2 = .4. LO5a. Find P1A0B2.b. Are A and B independent events?
For two events A and B, suppose P1A2 = .5, P1B2 = .8 and P1A ¨ B2 = .4. Find P1A ∪ B2. LO5
Given that P1A ¨ B2 = .3 and P1B0A2 = .9, find LO5 P(A).
Two events, A and B, are independent, with P1A2 = .5 and P1B2 = .3.a. Are A and B mutually exclusive? Why?b. Find P1A0B2 and P1B0A2. LO5c. Find P1A ∪ B2.
Find the numerical value ofa. 7!b. a8 7bc. a9 1bd. P53e. a7 4bf. 0!g. P93 h. P80
Going online for health information. A cyberchondriac is defined as a person who regularly searches the Web for health care information. A Harris Poll surveyed 1,010 U.S.adults by telephone and asked each respondent how often(in the past month) he or she looked for health care information online.
Beach erosional hot spots. Beaches that exhibit high erosion rates relative to the surrounding beach are defined as erosional hot spots. The U.S. Army Corps of Engineers is conducting a study of beach hot spots. Through an online questionnaire, data are collected on six beach hot spots.The data are
Toxic chemical incidents. Process Safety Progress (Sept.2004) reported on an emergency response system for incidents involving toxic chemicals in Taiwan. The system has logged over 250 incidents since being implemented.The next table gives a breakdown of the locations where these incidents
Federal civil trial appeals. The Journal of the American Law and Economics Association (Vol. 3, 2001) published the results of a study of appeals of federal civil trials. The accompanying table, extracted from the article, gives a breakdown of 2,143 civil cases that were appealed by either the
Winning at roulette. Roulette is a very popular game in many American casinos. In Roulette, a ball spins on a circular wheel that is divided into 38 arcs of equal length, bearing the numbers 00, 0, 1, 2,c, 35, 36. The number of the arc on which the ball stops is the outcome of one play of the game.
Cigar smoking and cancer. The Journal of the National Cancer Institute (Feb. 16, 2000) published the results of a study that investigated the association between cigar smoking and death from tobacco-related cancers. Data were obtained for a national sample of 137,243 American men.The results are
Elderly wheelchair user study. The American Journal of Public Health (Jan. 2002) reported on a study of elderly wheelchair users who live at home. A sample of 306 wheelchair users, age 65 or older, were surveyed about whether they had an injurious fall during the year and whether their home
Sociology fieldwork methods. Refer to University of New Mexico professor Jane Hood’s study of the fieldwork methods used by qualitative sociologists, presented in Exercise 2.195 (p. 136). Recall that she discovered that fieldwork methods could be classified into four distinct
Sex composition patterns of children in families. In having children, is there a genetic factor that causes some families to favor one sex over the other? That is, does having boys or girls “run in the family”? This was the question of interest in Chance (Fall 2001). Using data collected on
Bulimia study. The “fear of negative evaluation” (FNE)scores for 11 female students known to suffer from the eating disorder bulimia and 14 female students with normal eating habits, first presented in Exercise 2.44 (p. 80), are reproduced in the next table. (Recall that the higher the score,
Drug content assessment. Refer to Exercise 5.68 (p. 287)and the Analytical Chemistry (Dec. 15, 2009) study in which scientists used high-performance liquid chromatography todetermine the amount of drug in a tablet. Twenty-five tablets were produced at each of two different, independent sites. Drug
Does rudeness really matter in the workplace? A study in the Academy of Management Journal (Oct. 2007) investigated how rude behaviors influence a victim’s task performance.College students enrolled in a management course LO5 were randomly assigned to one of two experimental conditions:rudeness
Settlement of shallow foundations. Structures built on a shallow foundation (e.g., a concrete slab-on-grade foundation)are susceptible to settlement. Consequently, accurate settlement prediction is essential in the design of the foundation. Several methods for predicting settlement of shallow
Introduce the concepts of a test of hypothesis (8.1–8.2) LO9
Provide a measure of reliability for the hypothesis LO9 test—called the significance level of the test (8.2, 8.3)
Test a specific value of a population parameter LO9 (mean, proportion, or variance) (8.4–8.6, 8.8)
The effect of drugs and alcohol on the nervous system has been the subject of considerable research. Suppose a research neurologist is testing the effect of a drug on response time by injecting 100 rats with a unit dose of the drug, subjecting each LO9 that the mean response time for rats not
What is the difference between the null and the alternative LO9 hypothesis?
Which element of a test of hypothesis is used to decide whether to reject the null hypothesis in favor of the alternative LO9 hypothesis?
What is the size of a test of hypothesis? LO9
What are the different errors associated with a hypothesis testing problem? LO9
Give a real-life example of committing a Type I error and Type II error. LO9 LO9
If a right-tailed test is rejected at the 1% level of significance, do we need to test at the 5% level of significance? LO9 Why?
If the null hypothesis is not rejected, does that imply that it is true? Explain. LO9
Consider a test of H0: m = 5. In each of the following cases, give the rejection region for the test in terms of the z-statistic:a. Ha: m 7 5, a = .10b. Ha: m 7 5, a = .05c. Ha: m 6 5, a = .01d. Ha: m 5, a = .10 LO9
Consider the test of H0: m = 5. For each of the following, find the p-value of the test: LO9a. Ha: m 7 5, z = 3.16b. Ha: m 6 5, z = -3.16c. Ha: m 5, z = 3.16
If a hypothesis test were conducted using a = .05, for which of the following p-values would the null hypothesis be rejected? LO9a. .07b. .20c. .04d. .001e. .002f. .032
In a test of the hypothesis H0: m = 30 versus Ha: m 7 30, a LO9 sample of n = 100 observations possessed mean x = 29.3 and standard deviation s = 4. Find and interpret the pvalue for this test.
In a test of H0: m = 50 against Ha: m 7 50, the sample data yielded the test statistic z = 2.24. Find and interpret the LO9 p-value for the test.
In a test of the hypothesis H0: m = 20 versus Ha: m 20, a sample of n = 50 observations possessed mean x = 20.7 and standard deviation s = 3. Find and interpret the p-value for this test. LO9
In a test of H0: m = 100 against Ha: m 100, the sample LO9 data yielded the test statistic z = 2.17. Find the p-value for the test. LO9
Refer to the neurological response-time test set up in Example 8.3 (p. 405). The sample of 100 drug-injected rats yielded the results (in seconds) shown in Table 8.3. At LO9 a = .01, use these data to conduct the test of hypothesis, H0: m = 1.2 Ha: m 1.2 Carrying out a Hypothesis Test for
Find the observed significance level (p-value) for the test of the mean drug response time in Examples 8.3 and 8.5. Interpret the result. LO9
Knowledge of the amount of time a patient occupies a hospital bed—called length of stay (LOS)—is important for allocating resources. At one hospital, the mean LOS was determined to be 5 days. A hospital administrator believes the mean LOS may now be less than 5 days due to a newly adopted
Which condition ensures normality of the sample mean in LO9 large samples?
For what values of the test statistic do you reject H0? fail to LO9 reject H0?
Use the applet entitled Hypotheses Test for a Mean to investigate the effect of the underlying distribution on the proportion of Type I errors. For this exercise, take n = 100, mean = 50, LO9 standard deviation = 10, null mean = 50, and alternative 6 .a. Select the normal distribution and run the
Use the applet entitled Hypotheses Test for a Mean to investigate the effect of the underlying distribution on the proportion of Type II errors. For this exercise, take n = 100, mean = 50, LO9 standard deviation = 10, null mean = 52, and alternative 6 .a. Select the normal distribution and run the
Use the applet entitled Hypotheses Test for a Mean to investigate the effect of the null mean on the probability of making LO9 a Type II error. For this exercise, take n = 100, mean = 50,standard deviation = 10, and alternative 6 with the normal distribution.Set the null mean to 55 and run the
Speeding and young drivers. Psychologists conducted a survey of 258 student drivers and their attitudes toward speeding and reported the results in the British Journal of Educational Psychology (Vol. 80, 2010). One of the variables of interest was the response to the question, “Are LO9 you
Bone fossil study. Archeologists have found that humerus bones from the same species of animal tend to have approximately the same length-to-width ratios. It is known that species A exhibits a mean ratio of 8.5. Suppose 41 fossils of humerus bones were unearthed at an archeological site in East
Cooling method for gas turbines. A popular cooling method for a gas turbine engine uses high-pressure inlet fogging. The performance of a sample of 67 gas turbines augmented with high-pressure inlet fogging was investigated in the Journal of Engineering for Gas Turbines and Power (Jan. 2005). One
Time required to complete a task. When asked, “How much time will you require to complete this task?”, cognitive theory posits that people will typically underestimate the time required. Would the opposite theory hold if the question was phrased in terms of how much work could be completed in a
Instructing English-as-a-first-language learners. A study published in the journal Applied Linguistics (Feb. 2014)investigated the effects of implicit and explicit classroom interventions during the instruction of Japanese to Englishas-a-first-language (EFL) students. EFL students at a Japanese
A major car manufacturer wants to test a new engine to determine whether it meets new air-pollution standards. The mean emission m of all engines of this type must be less than 20 parts per million of carbon. Ten engines are manufactured for testing purposes, and the emission level of each is
Find the observed significance level for the test described in Example 8.8. LO9 Interpret the result.
When do we use the t-test instead of the z-test in small samples? LO9
What are the assumptions behind a t-test in testing a hypothesis LO9 about a population mean?
For each of the rejection regions defined in Exercise 8.53, what is the probability that a Type I error will be made? LO9
A sample of five measurements, randomly selected from a normally distributed population, resulted in the following summary statistics: x = 4.8, s = 1.3. LO9a. Test the null hypothesis that the mean of the population is 6 against the alternative hypothesis, m 6 6. Use a = .05.b. Test the null
Lobster trap placement. Refer to the Bulletin of Marine Science (Apr. 2010) observational study of lobster trap placement by teams fishing for the red spiny lobster in Baja California Sur, Mexico, Exercise 7.41 (p. 363). Trap spacing measurements (in meters) for a sample of seven LO9 teams of red
Music performance anxiety. Refer to the British Journal of Music Education (Mar. 2014) study of performance anxiety by music students, Exercise 7.37 (p. 362). Recall that the Performance Anxiety Inventory (PAI) was used to measure music performance anxiety on a scale from 20 to 80 points. The table
Crab spiders hiding on flowers. 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 2.42 (p. 79). Researchers at the French Museum of Natural History collected a sample of 10 adult female
Cheek teeth of extinct primates. Refer to the American Journal of Physical Anthropology (Vol. 142, 2010) study of the characteristics of cheek teeth (e.g., molars) in an LO9 extinct primate species, Exercise 2.38 (p. 78). Recall that the researchers recorded the dentary depth of molars(in
Radon exposure in Egyptian tombs. Refer to the Radiation Protection Dosimetry (Dec. 2010) study of radon exposure in Egyptian tombs, Exercise 7.39(p. 362). The radon levels—measured in becquerels per cubic meter (Bq/m3)—in the inner chambers of a sample of 12 tombs are listed in the table. For
Free recall memory strategy. Psychologists who study memory often use a measure of “free recall” (e.g., the number of correctly recalled items in a list of to-beremembered items). The strategy used to memorize the list—for example, category clustering—is often just as important. Researchers
Establish that a sample statistic is a random variable with a probability distribution (6.1)
Define a sampling distribution as the probability distribution of a sample statistic (6.1)
Give two important properties of sampling distributions (6.2)
Learn that the sampling distribution of both the sample mean and the sample proportion tends to be approximately normal (6.3, 6.4)
Consider the popular casino game of craps, in which a player throws two dice and bets on the outcome (the sum total of the dots showing on the upper faces of the two dice). In Example 4.5 (p. 218), we looked at the possible outcomes of a $5 wager on the first toss (called the come-out roll). Recall
Minimizing tractor skidding distance. Refer to the Journal of Forest Engineering (July 1999) study of minimizing tractor skidding distances along a new road in a European forest, presented in Exercise 7.48 (p. 364). The skidding distances (in meters) were measured at 20 randomly selected road
Dissolved organic compound in lakes. The level of dissolved oxygen in the surface water of a lake is vital to maintaining the lake’s ecosystem. Environmentalists from the University of Wisconsin monitored the dissolved oxygen levels over time for a sample of 25 lakes in the state (Aquatic
The rolling machine of a steel manufacturer produces sheets of steel of varying thickness. The thickness of a steel sheet follows a uniform distribution with values between 150 and 200 millimeters. Suppose we perform the following experiment over and over again: Randomly sample 11 steel sheets from
What is the difference between a population parameter and a sample statistic? LO6
What is a sampling distribution of a sample statistic? LO6
Walking straight into circles. When people get lost in unfamiliar terrain, do they really walk in circles, as is commonly believed? To answer this question, researchers conducted a field experiment and reported the results in Current Biology (Sept. 29, 2009). Fifteen volunteers were blindfolded and
The probability distribution shown here describes a population of measurements that can assume values of 0, 2, 4, and 6, each of which occurs with the same relative frequency:x 0 2 4 6 p1x2 1 4 1 4 1 4 1 4a. List all the different samples of n = 2 measurements that can be selected from this
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 .3 .2 .3 .2 Sample Probability Sample Probability 0, 0 .09 2, 0 .09 0, 1 .06 2, 1 .06 0, 2 .09 2, 2 .09 0, 3 .06 2, 3 .06 1, 0 .06 3, 0
The reputations (and hence sales) of many businesses can be severely damaged by shipments of manufactured items that contain a large percentage of defectives. For example, a manufacturer of alkaline batteries may want to be reasonably certain that less than 5% of its batteries are defective.
Refer to Exercise 6.5 and find E1x2 = m. Then use the sampling distribution of x found in Exercise 6.5 to find the expected value of x. Note that E1x2 = m. LO6
In Example 8.10, we found that we did not have sufficient evidence at the a = .01 level of significance to indicate that the fraction defective, p, of alkaline batteries was less than p = .05. How strong was the weight of evidence favoring the LO9 alternative hypothesis 1Ha: p 6 .052? Find the
Which statistical distribution is typically associated with making inferences about a population proportion p? LO9
What are the assumptions for a valid large-sample test LO9 for p?
Suppose two statistics, A and B, exist to estimate the same population parameter u (theta). (Note that u could be any parameter: m, s2, s, etc.) Suppose the two statistics have sampling distributions as shown in Figure 6.6. On the basis of these sampling LO6 distributions, which statistic is more
Refer to Example 6.2 and the outcome x of a $5 wager in craps. We found the sampling distributions of the sample mean x and the sample median M for random samples of n = 3 dice rolls from a population defined by the following probability distribution:x -5 0 5 LO6 p1x2 1 9 6 9 2 9 The sampling
Refer to Example 6.5 and find the standard deviations of the sampling distributions of x and M. Which statistic would appear to be a better estimator of m? LO6
What is a point estimator of a population parameter? LO6
What is the difference between a biased and unbiased LO6 estimator?
What is the MVUE for a parameter? LO6
What are the properties of an ideal estimator? LO6
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