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A First Course In Statistics 12th Edition James T McClave, Terry T Sincich - Solutions
For each of the following 99% confidence intervals for b1 in simple linear regression, decide whether there is evidence of a positive or negative linear relationship between y and x.a. (8, 80)b. 1 -51, -132c. 1 -37, 1032 Learning the Mechanics
Life tests of cutting tools. To improve the quality of the output of any production process, it is necessary first to understand the capabilities of the process. (For example, see Gitlow, H., Quality Management Systems: A Practical Guide, 2000.) In a particular manufacturing process, the useful
Ideal height of your mate. Refer to the Chance (Summer 2008) study of the height of the ideal mate, Exercise 9.33(p. 540). The data were used to fit the simple linear regression model, E1y2 = b0 + b1x, where y = ideal partner’s height (in inches) and x = student’s height (in inches).a. Fit the
Sweetness of orange juice. Refer to the study of the quality of orange juice produced at a juice manufacturing plant, Exercise 9.32 (p. 540). Recall that simple linear regression was used to predict the sweetness index (y) from the amount of pectin (x) in orange juice manufactured during a
FCAT scores and poverty. Refer to the Journal of Educational and Behavioral Statistics (Spring 2004) study of scores on the Florida Comprehensive Assessment Test(FCAT), presented in Exercise 9.30 (p. 539).a. Consider the simple linear regression relating math score (y) to percentage (x) of students
Detecting rapid visual targets. When two targets are presented close together in a rapid visual stream, the second target is often missed. Psychologists call this phenomenon the attentional blink (AB). A study published in Advances in Cognitive Psychology (July 2013) investigated whether
Mongolian desert ants. Refer to the Journal of Biogeography (Dec. 2003) study of ant sites in Mongolia, presented in Exercise 9.26 (p. 538). The data were used to estimate the straight-line model relating annual rainfall (y)to maximum daily temperature (x).a. Give the values of SSE, s2, and s,
Quantitative models of music. Chance (Fall 2004) published a study on modeling a certain pitch of a musical composition. Data on 147 famous compositions were used to model the number of times (y) a certain pitch occurs—called entropy—as a straight-line function of year of birth(x) of the
New method for blood typing. Refer to the Analytical Chemistry (May 2010) study in which medical researchers tested a new method of typing blood using low-cost paper, Exercise 9.25 (p. 538). The data were used to fit the straight-line model relating y = wicking length to x = antibody concentration.
Game performance of water polo players. Refer to the Biology of Sport (Vol. 31, 2014) study of the physiological performance of top-level water polo players, Exercise 9.24(p. 537). Recall that data for eight Olympic male water polo players were used to model y = mean heart rate as a straight-line
Measuring the moon’s orbit. Refer to the American Journal of Physics (Apr. 2014) study of the moon’s orbit, Exercise 9.23 (p. 537). Recall that the angular size (y)of the moon was modeled as a straight-line function of height above horizon (x). Find an estimate of s, the standard deviation of
Do nice guys really finish last? Refer to the Nature (Mar. 20, 2008) study of whether “nice guys finish last,” Exercise 9.22(p. 536). Recall that Boston-area college students repeatedly played a version of the game “prisoner’s dilemma,”where competitors choose cooperation, defection, or
Refer to Exercises 9.18 and 9.21 (p. 536). Calculate SSE, s2, and s for the least squares lines obtained in those exercises.Interpret the standard errors of the regression model for each.Applying the Concepts—Basic
Suppose you fit a least squares line to 12 data points and the calculated value of SSE is .429.a. Find s2, the estimator of s2 (the variance of the random error term e).b. Find s, the estimate of s.Exercises 9.37–9.52c. What is the largest deviation that you might expect between any one of the 12
Calculate SSE and s2 for each of the following cases:a. n = 25, SSyy = 110, SSxy = 60, b n1 = .80b. n = 50, ay2 = 900, ay = 90, SSxy = 2 5 0 0 , b n1 = .2 5c. n = 25, a1yi - y22 = 75, SSxy = 100, SSxx = 200
Visually compare the scatterplots shown below. If a least squares line were determined for each data set, which do you think would have the smallest variance s2? Explain.5 10 15 x xa. y 10 515 5 10 15b. y c.10 515 5 10 15 xy 10 515 Learning the Mechanics
Forecasting movie revenues with Twitter. Marketers are keenly interested in how social media (e.g., Facebook, Twitter) may influence consumers who buy their products.Researchers at HP Labs (Palo Alto, CA) investigated whether the volume of chatter on Twitter.com could be used to forecast the box
Spreading rate of spilled liquid. Refer to the Chemical Engineering Progress (Jan. 2005) study of the rate at which a spilled volatile liquid will spread across a surface, presented in Exercise 2.168 (p. 121). Recall that a DuPont Corp. engineer calculated the mass (in pounds) of a 50-gallon
The “name game.” Refer to the Journal of Experimental Psychology—Applied (June 2000) study in which the“name game” was used to help groups of students learn the names of other students in the group, Exercise 7.120(p. 458). [In the “name game” student #1 states his/her full name,
Ideal height of your mate. Anthropologists theorize that humans tend to choose mates who are similar to themselves.This includes choosing mates who are similar in height. To test this theory, a study was conducted on 147 Cornell University students (Chance, Summer 2008). Each student was asked to
Sweetness of orange juice The quality of the orange juice produced by a manufacturer is constantly monitored.There are numerous sensory and chemical components that combine to make the best-tasting orange juice. For example, one manufacturer has developed a quantitative index of the “sweetness”
Sound waves from a basketball. Refer to the American Journal of Physics (June 2010) study of sound waves in a spherical cavity, Exercise 2.43 (p. 76). The frequencies of sound waves (estimated using a mathematical formula)resulting from the first 24 resonances (echoes) after striking a basketball
Ranking driving performance of professional golfers.Refer to The Sport Journal (Winter 2007) study of a new method for ranking the total driving performance of golfers on the Professional Golf Association (PGA) tour, presented in Exercise 2.66 (p. 86). Recall that the methoda. Propose a
Repair and replacement costs of water pipes. Pipes used in a water distribution network are susceptible to breakage due to a variety of factors. When pipes break, engineers must decide whether to repair or replace the broken pipe. A team of civil engineers used regression analysis to estimate y =
FCAT scores and poverty. In the state of Florida, elementary school performance is based on the average score obtained by students on a standardized exam called the Florida Comprehensive Assessment Test (FCAT). An analysis of the link between FCAT scores and sociodemographic factors was published
Ranking driving performance of professional golfers.Refer to The Sport Journal (Winter 2007) study of a new method for ranking the total driving performance of golfers on the Professional Golf Association (PGA) tour, presented in Exercise 2.66 (p. 86). Recall that the method computes a driving
Repair and replacement costs of water pipes. Pipes used in a water distribution network are susceptible to breakage due to a variety of factors. When pipes break, engineers must decide whether to repair or replace the broken pipe. A team of civil engineers used regression analysis to estimate y =
Redshifts of quasi-stellar objects. Astronomers call a shift in the spectrum of galaxies a “redshift.” A correlation between redshift level and apparent magnitude(i.e., brightness on a logarithmic scale) of a quasi-stellar object was discovered and reported in the Journal of Astrophysics &
Mongolian desert ants. Refer to the Journal of Biogeography(Dec. 2003) study of ants in Mongolia, presented in Exercise 2.167 (p. 121). Data on annual rainfall, maximum daily temperature, and number of ant species recorded at each of 11 study sites are listed in the table.Site Region Annual
New method for blood typing. Refer to the Analytical Chemistry (May 2010) study in which medical researchers tested a new method of typing blood using low-cost paper, Exercise 2.163 (p. 120). The researchers applied blood drops to the paper and recorded the rate of absorption(called blood wicking).
Game performance of water polo players. The journal Biology of Sport (Vol. 31, 2014) published a study of the physiological performance of top-level water polo players.Eight Olympic male water polo players participated in the study. Two variables were measured for each during competition: y = mean
Measuring the moon’s orbit. A handheld digital camera was used to photograph the moon’s orbit and the results summarized in the American Journal of Physics (Apr.2014). The pictures were used to measure the angular size(in pixels) of the moon at various distances (heights) above the horizon
Do nice guys really finish last? In baseball, there is an old saying that “nice guys finish last.” Is this true in the competitive corporate world? Researchers at Harvard University attempted to answer this question and reported their results in Nature (Mar. 20, 2008). In the study, Boston-area
Use the applet entitled Regression by Eye to explore the relationship between the pattern of data in a scatterplot and the corresponding least squares model.a. Run the applet several times. For each time, attempt to move the green line into a position that appears to minimize the vertical distances
Consider the following pairs of measurements.x 5 3 -1 2 7 6 4 y 4 3 0 1 8 5 3a. Construct a scatterplot of these data.b. What does the scatterplot suggest about the relationship between x and y?c. Given that SSxx = 43.4286, SSxy = 39.8571, y = 3.4286, and x = 3.7143, calculate the least squares
Construct a scatterplot of the following data.x .5 1 1.5 y 2 1 3a. Plot the following two lines on your scatterplot:y = 3 - x and y = 1 + xb. Which of these lines would you choose to characterize the relationship between x and y? Explain.c. Show that the sum of errors for both of these lines equals
Refer to Exercise 9.18. After the least square line has been obtained, the following table can be used (1) to compare the observed and predicted values of y and (2) to compute SSE.x y yn 1y - yn2 1y - yn22 1 8 — — —7 3 — — —9 10 — — —6 9 — — —9 10 — — —10 10 — —
The accompanying table is used to make the preliminary computations for finding the least squares line for the given pairs of x and y values.a. Complete the table.c. Find SS xxe. Find x and y. g. Find the least squares line.b. Find SSxy-d. Find B.f. Find B. [Hint: Use the formulas in the box on p.
True or False. The estimates of b0 and b1 should be interpreted only within the sampled range of the independent variable, x.Learning the Mechanics
Give the slope and y-intercept for each of the lines defined in Exercise 9.9.Applying the Concepts—Basic
Plot the following lines.a. y = 2 + xb. y = 3 - 4xc. y = -3 + 4xd. y = -2xe. y = xf. y = .55 + 2.5x
Refer to Exercise 9.7. Find the equations of the lines that pass through the points listed in Exercise 9.5.
Give the slope and y-intercept for each of the lines graphed in Exercise 9.5.
If a straight-line probabilistic relationship relates the mean E(y) to an independent variable x, does it imply that every value of the variable y will always fall exactly on the line of means? Why or why not?Learning the Mechanics
A “rigged” election? Chance (Spring 2004) presented data from a recent election held to determine the board of directors of a local community. There were 27 candidates for the board, and each of 5,553 voters was allowed to choose 6 candidates. The claim was that “a fixed vote with fixed
Testing normality. Suppose a random variable is hypothesized to be normally distributed with a mean of 0 and a standard deviation of 1. A random sample of 200 observations of the variable yields frequencies in the intervals listed in the table shown at the bottom of the page. Do the data provide
Goodness-of-fit test. A statistical analysis is to be done on a set of data consisting of 1,000 monthly salaries. The analysis requires the assumption that the sample was drawn from a normal distribution. A preliminary test, called the x2 goodness-of-fit test, can be used to help determine whether
Gambling in public high schools. With the rapid growth in legalized gambling in the United States, there is concern that the involvement of youth in gambling activities is also increasing. University of Minnesota professor Randy Stinchfield compared the annual rates of gambling among Minnesota
Guilt in decision making. The effect of guilt emotion on how a decision maker focuses on the problem was investigated in the Jan. 2007 issue of the Journal of Behavioral Decision Making. A total of 171 volunteer students participated in the experiment, where each was randomly assigned to one of
Subarctic plant study. The traits of seed-bearing plants indigenous to subarctic Finland were studied in Arctic, Antarctic, and Alpine Research (May 2004). Plants were categorized according to type (dwarf shrub, herb, or grass), abundance of seedlings (no seedlings, rare seedlings, or abundant
IQ and mental deficiency. A person is diagnosed with a mental deficiency if, before the age of 18, his/her score TRENCH MDIQ Table for Exercise 8.101 CAHS Level Low Medium High Very High Totals Low 32 14 2 0 48 SHSS: C Level Medium 11 14 6 0 31 High 6 14 19 3 42 Very High 0 2 4 3 9 Totals 49 44 31
Flight response of geese to helicopter traffic. Offshore oil drilling near an Alaskan estuary has led to increased air traffic—mostly large helicopters—in the area. The U.S.Fish and Wildlife Service commissioned a study to investigate the impact these helicopters have on the flocks of Pacific
Multiple sclerosis drug. Interferons are proteins produced naturally by the human body that help fight infections and regulate the immune system. A drug developed from interferons, called Avonex, is now available for treating patients with multiple sclerosis (MS). In a clinical study, 85 MS
Masculinity and crime. Refer to the Journal of Sociology(July 2003) study on the link between the level of masculinity and criminal behavior in men, presented in Exercise 7.25(p. 410). The researcher identified events that a sample of newly incarcerated men were involved in and classified each
Killing insects with low oxygen. Refer to the Journal of Agricultural, Biological, and Environmental Statistics (Sept.2000) study of the mortality of rice weevils exposed to low oxygen, presented in Exercise 6.92 (p. 370). Recall that 31,386 of 31,421 rice weevils were found dead after exposure to
Purchasing souvenirs. A major tourist activity is shopping.Travel researchers estimate that nearly one-third of total travel expenditures are used on shopping for souvenirs(Journal of Travel Research, May 2011). To investigate the impact of gender on souvenir shopping, a survey of 3,200 tourists
Refer to the Family and Consumer Sciences Research Journal (Mar. 2005) study of college students and drinking, Exercise 8.91. A second objective of the researchers was to establish a statistical link between the frequency of drinking(none, once per month, twice per week, or more) and the amount of
Sociology fieldwork methods. Refer to the Teaching Sociology (July 2006) study of the fieldwork methods used by qualitative sociologists, presented in Exercise 2.193 (p. 132). Recall that fieldwork methods can be categorized as follows: Interview, Observation plus Participation, Observation Only,
Politics and religion. University of Maryland professor Ted R. Gurr examined the political strategies used by ethnic groups worldwide in their fight for minority rights (Political Science & Politics, June 2000). Each in a sample of 275 ethnic groups was classified according to world region and
Racial profiling by the LAPD. Racial profiling is a term used to describe any police action that relies on ethnicity rather than behavior to target suspects engaged in criminal activities. Does the Los Angeles Police Department(LAPD) invoke racial profiling in stops and searches of Los Angeles
Excavating ancient pottery. Refer to the Chance (Fall 2000) study of ancient Greek pottery, presented in Exercise 2.186 (p. 130). Recall that 837 pottery pieces were uncovered at the excavation site. The table describing the types of pottery found is reproduced here.Pot Category Number Found
Safety of hybrid cars. According to the Highway Loss Data Institute (HLDI), “hybrid [automobiles] have a safety edge over their conventional twins when it comes to shielding their occupants from injuries in crashes” (HLDI Bulletin, Sept. 2011). Consider data collected by the HLDI on Honda
Oil spill impact on seabirds. Refer to the Journal of Agricultural, Biological, and Environmental Statistics(Sept. 2000) study of the impact of a tanker oil spill on the seabird population in Alaska, presented in Exercise 2.201 (p. 133). Recall that for each of 96 shoreline locations(called
A random sample of 250 observations was classified according to the row and column categories shown in the following table:Column 1 2 3 1 30 30 10 Row 2 10 20 60 3 20 60 10a. Do the data provide sufficient evidence to conclude that the rows and columns are dependent? Test, using a = .05.b. Would
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 1 Sample 2 n1 = 200 n2 = 200 x1 = 110 x2 = 130a. Test H0: 1p1 - p22 = 0 against Ha: 1p1 - p22 6 0.Use a = .10.b. Form a 95%
What is the difference between a one-way chi-square analysis and a two-way chi-square analysis?Learning the Mechanics
Examining the “Monty Hall Dilemma.” In Exercise 3.145(p. 188) you solved the game show problem of whether to switch your choice of three doors, one of which hides a prize, after the host reveals what is behind a door that is not chosen. (Despite the natural inclination of many to keep one’s
Efficacy of an HIV vaccine. New, effective AIDS vaccines have been developed through the process of “sieving”—that is, sifting out infections with some strains of HIV. Consider a vaccine designed to eliminate a particular strain of the virus.To test the efficacy of the vaccine, a clinical
Interactions in a children’s museum. Refer to the Early Childhood Education Journal (Mar. 2014) study of interactions in a children’s museum, Exercise 8.51 (p. 493).Summary information for the 170 meaningful interactions sampled is reproduced in the following table. Do the proportions
Reading comprehension of Texas students. An analysis of reading test scores of students at a rural Texas school district was carried out in Current Issues in Education(Jan. 2014). Students were classified as attending elementary, middle, or high school and whether they passed a reading
Classifying air threats with heuristics. The Journal of Behavioral Decision Making (Jan. 2007) published a study on the use of heuristics to classify the threat level of approaching aircraft. Of special interest was the use of a fast and frugal heuristic—a computationally simple procedure for
Mobile device typing strategies. Refer to the Applied Ergonomics (Mar. 2012) study of mobile device typing strategies, Exercise 8.46 (p. 491). Recall that typing style of mobile device users was categorized as (1) device held with both hands/both thumbs typing, (2) device held with right hand/right
Detecting Alzheimer’s disease at an early age. Refer to the Neuropsychology (Jan. 2007) study of whether the cognitive effects of Alzheimer’s disease can be detected at an early age, Exercise 8.49 (p. 492). Recall that a particular strand of DNA was classified into one of three genotypes:E4
Job satisfaction of women in construction. The hiring of women in construction and construction-related jobs has steadily increased over the years. A study was conducted to provide employers with information designed to reduce the potential for turnover of female employees (Journal of Professional
Influencing performance in a serial addition task.Refer to the Advances in Cognitive Psychology (Jan.2013) study of performance in a classic psychological test involving adding a set of numbers, Exercise 8.12(p. 480). Recall that 300 undergraduate students were given a serial addition task, with
“Cry wolf” effect in air traffic controlling. Researchers at Alion Science Corporation and New Mexico State University collaborated on a study of how air traffic controllers respond to false alarms (Human Factors, Aug. 2009). The researchers theorize that the high rate of false alarms regarding
Package design influences taste. Can the package design of a food product influence how the consumer will rate the taste of the product? A team of experimental psychologists reported on a study that examined how rounded or angular package shapes and high- or low-pitched sounds can convey
Healing heart patients with music, imagery, touch, and prayer. “Frontier medicine” is a term used to describe medical therapies (e.g., energy healing, therapeutic prayer, spiritual healing) for which there is no plausible explanation.The Lancet (July 16, 2005) published the results of a study
Stereotyping deceptive and authentic news stories. Major newspapers lose their credibility (and subscribers) when they are found to have published deceptive or misleading news stories. In Journalism and Mass Communication Quarterly (Summer 2007), University of Texas researchers investigated whether
Eyewitnesses and mug shots. Applied Psychology in Criminal Justice (Apr. 2010) published a study of mug shot choices by eyewitnesses to a crime. A sample of Exercise 10.107 (p. 594). A sample of 96 college students was shown a video of a simulated theft, then asked to select the mug shot that most
Children’s perceptions of their neighborhood. In Health Education Research (Feb. 2005), nutrition scientists at Deakin University (Australia) investigated children’s perceptions of their environments. Each in a sample of 147 ten-year-old children drew maps of their home and neighborhood
Refer to Exercise 8.61. Convert the responses to percentages by calculating the percentage of each B class total falling into each A classification. Also, calculate the percentage of the total number of responses that constitute each of the A classification totals.a. Create a bar graph with row A1
Refer to Exercise 8.59.a. Convert the frequency responses to percentages by calculating the percentage of each column total falling in each row. Also, convert the row totals to percentages of the total number of responses. Display the percentages in a table.b. Create a bar graph with row 1
Find the rejection region for a test of independence of two classifications where the contingency table contains r rows and c columns.a. a = .05, r = 5, c = 6b. a = .10, r = 5, c = 3a. a = .01, r = 2, c = 5
What conditions are required for a valid chi-square test of data from a contingency table?Exercises 8.54–8.78 Learning the Mechanics
What is a two-way (contingency) table?
Political representation of religious groups. Do those elected to the U.S. House of Representatives really “represent”their constituents demographically? This was a question of interest in Chance (Summer 2002). One of several demographics studied was religious affiliation.The table in the next
Interactions in a children’s museum. Refer to the Early Childhood Education Journal (Mar. 2014) study of interactions in a children’s museum, Exercise 2.19 (p. 65).Recall that interactions by visitors to the museum were classified as (1) show-and-tell, (2) learning/teaching, (3)refocusing, (4)
Traffic sign maintenance. Refer to the Journal of Transportation Engineering (June 2013) study of traffic sign maintenance, Exercise 8.17 (p. 481). Recall that civil engineers estimated the proportion of traffic signs maintained by the North Carolina Department of Transportation (NCDOT) that fail
Characteristics of ice-melt ponds. The National Snow and Ice Data Center (NSIDC) collected data on 504 ice-melt ponds in the Canadian Arctic. One variable of interest to environmental engineers studying the ponds is the type of ice observed in each. Ice type is classified as first-year ice,
Curbing street gang gun violence. Refer to the Journal of Quantitative Criminology (Mar. 2014) study of street gun violence in Boston, Exercise 2.18 (p. 65). Recall that over a 5-year period (2006–2010), 80 shootings involving a Boston street gang were sampled and analyzed. Of these, 37 occurred
Gender in two-child families. Refer to the Human Biology(Feb. 2009) study on the gender of children in two-child families, Exercise 4.33 (p. 204). The article reported on the results of the National Health Interview Survey (NHIS) of 42,888 two-child families. The table below gives the number of
Museum management. Refer to the Museum Management and Curatorship (June 2010) worldwide survey of 30 leading museums of contemporary art, Exercise 2.22 (p. 65). Recall that each museum manager was asked to provide the performance measure used most often for internal evaluation. A summary of the
Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of how engineers design social robots, Exercise 2.7 (p. 62).Recall that a social (or service) robot is designed to entertain, educate, and care for human users. In a random sample of 106
A multinomial experiment with k = 4 cells and n = 400 produced the data shown in the accompanying table. Do these data provide sufficient evidence to contradict the null hypothesis that p1 = .2, p2 = .4, p3 = .1, and p4 = .3?Test, using a = .05.Cell 1 2 3 4 ni 64 156 41 139 Applying the
Find the rejection region for a one-dimensional x2-test of a null hypothesis concerning p1, p2,…, pk ifa. k = 11; a = .01b. k = 9; a = .01c. k = 6; a = .05
What conditions must n satisfy to make the x2 test for a one-way table valid?Learning the Mechanics
Cable-TV home shoppers. 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
Buyers of TVs. A manufacturer of large-screen televisions wants to compare with a competitor the proportions of its best sets that need repair within 1 year. If it is desired to estimate the difference between proportions to within .05 with 90% confidence, and if the manufacturer plans to sample
Influencing performance in a serial addition task. Refer to the Advances in Cognitive Psychology (Jan. 2013) study of influencing performance in a classic psychological test that involved adding a set of numbers, Exercise 8.12(p. 480). Recall that one group of students saw each of the numbers for 2
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