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statistics principles and methods

Statistics Principles And Methods 8th Edition Richard A. Johnson, Gouri K. Bhattacharyya - Solutions

Given the data,(a) Fit a quadratic curve using the equations on page 391.(b) Verify your answers using software.R: summary(lm(y ~ x + x2)) where x and y contain the observations and x2= x*x у -3 -2 5 10 -1 0 1 3 4 13 2 12 3 23 со
An interested student used the method of least squares to fit the straight line ŷ = 850. 7 + 320.3 x to gross domestic product, y, in real dollars. The results for 26 recent years, x = I, 2, ... , 26, appear here. Which assumption for a linear regression model appear to be seriously violated by
Listed below are the price quotations on an Internet site for a midsize foreign used car along with their age and odometer mileage.Perform a multiple regression analysis of these data. In particular(a) Determine the equation for predicting the price from age and mileage. Interpret the meaning of
Internet consumer ratings of the previous model smart speaker, based on about 100,000 ratings, can b e summarized as:The ratings of the new model by 200 persons yielded the following frequency table.Do these data show a significantly different distribution of ratings than the previous mode P Test
A group of eight students want to compare the quality of food at 4 campus area restaurants. The two students randomly assigned to a site, dine on different nights. Each student rates the quality of their meal on a ten point scale. Calling the restaurant the treatment, suppose the results are(a)
A strategy called A/B testing is being implemented by many e-commerce firms. A product web page is modified by adding a picture or other visual change. Then, a fraction of the traffic is routed to the new page. For a sample of 1000 consumers who visit the original page, 70 purchase the item. From a
Subjects must press a button when they h ear a signal. The three treatments are three different intensities of the signal. The time elapsed between presentation of the signal and when the button is pushed, are recorded in hundredths of a second. Suppose the data are(a) Obtain the arrays that show a
Referring to Exercise 13.10, compare the conclusions of the level α = .05(a) χ2 test of homogeneity.(b) Z test that sales are higher with the modified page.Data from in Exercise 13.10A strategy called A/B testing is being implemented by many e-commerce firms. A product web page is modified
Reading levels vary between different magazines. To avoid difficulties caused by different typefaces and sizes, an investigator just counted the number of letters and punctuation signs. Random samples of 20 sentences were selected from The New Yorker, Sports Illustrated, and National Geographic.
An investigator wonders how the frequency of checking a smart phone varies with current activity. Students are assigned to one of four conditions: listening to a lecture, studying, eating a meal, or on a date. The response they record is the number of times in one hour that they check their phone
Test for equality of means based on the data in Exercise 14.2. Take a = .05.Data from in Exercise 14.2Subjects must press a button when they h ear a signal. The three treatments are three different intensities of the signal. The time elapsed between presentation of the signal and when the button is
The yield, in pounds, of three types of heritage tomatoes (treatments) is obtained after planting them in three equal sized plots within a site (block) . Types are randomly assigned to plots. A total of four different sites are used. Suppose the data are(a) Provide a decomposition for the
The hours of relief are measured under a placebo, Brand A, and Brand B sinus medicines. Call these treatment 1, treatment 2, and treatment 3, respectively. They are each given in succession, in random order, to each subject with two days between each treatment. Suppose the data are (a) Provide
Food scientists investigated whether making a cheese sauce by a continuous process or batch process made any difference to taste. They also included a third treatment, a carefully selected ideal product, that served as a control. Treatment I is the ideal, treatment 2 is the continuous process, and
One aspect of a study of gender differences involves the play behavior of monkeys during the first year of life (courtesy of H. Harlow, U. W. Primate Laboratory). Six male and six female monkeys are observed in groups of four families during several ten-minute test sessions. The mean tot al number
In a taste test of two chocolate chip cookie recipes, 13 out of 17 subjects favored recipe A. Using the sign test, find the significance probability when H1 states that recipe A is preferable.
Refer to Exercise 10.67. Evaluate:(a) Sign test statistic.(b) Signed-rank statistic.Data from in Exercise 10.67A sample of river water is divided into two specimens. One is randomly selected to be sent to Lab A and the other is sent to Lab B. This is repeated for a total of nine times. The
Twelve bicycles are available for use at the student union. Use Table 1, Appendix B, to select 4 of them for you and three of your friends to ride today.Data from in Table 1 Appendix B TABLE 1 Random Digits Row 1 5925 0695 7741 8254 4297 0000 5277 6563 9265 1023 9088 5744 4790 2 0437 3 6242 5434
A survey of 451 men revealed that 144 men, or 3 1.9%, wait until Valentine's day or the day before to purchase flowers. Identify a statistical population and the sample.
A social networking site reported the number of passwords memorized by 150 visitors who agreed to participate. Identify the statistical population and the sample for the number of passwords memorized.
Twenty college students were asked for their number of close friends; persons who showed sympathy when needed and helped in hard times. The average number reported was just over 2. Identify a statistical population and the sample.
The article What Makes a Great Tweet concludes that only 36% of tweets are worth reading. A total of 4,220 tweets were rated in this study. Identify a statistical population and the sample.
Among 40 adults 20- 25 years old questioned about stress levels, 16 responded they are more stressed now than last year. Identify a statistical population and the sample.
Rap music was the favorite genre of 6 out of 56 students from a large midwestern university. Identify a statistical population and the sample.
About 42% of the members of a local hiking club own a dog. Should these people be considered as a random sample of dog ownership for persons living in the city?
At the last minute, 6 tickets have become available for a big football game. Use Table 1, Appendix B, to select the recipients from among 89 interested students.Data from in Table 1 Appendix B TABLE 1 Random Digits Row 1 2 5925 4790 0695 7741 8254 4297 0000 5277 6563 9265 1023 0437 5434 8503
Give a statement of purpose for a study to determine the favorite campus area pizza establishment.
Give a statement of purpose for determining the amount of time it takes to make hotel reservations in San Francisco using the internet.
How many of the calls in the initial dat a set took over 125 minutes to answer? How many over 90 minutes?
A newspaper headline reads, College Students Display An Inability To Tell Fake News from Real and the article explains this conclusion was reached from the responses of 2300 students at ten colleges concerning whether or not a case of social media type news was fake or not.(a) Specify the variable
The number of hours actively connected to social media on the previous day are recorded for 120 students at a university. Identify the population unit, statistical population, and sample.
It is often easy to put off doing an unpleasant task. At a Web site, persons can take a test and receive a score that determines if they have a serious problem with procrastination. Should the scores from people who take this test online be considered a random sample from the general population?
The United States Environmental Protection Agency? reports that in 2014, each American generated 4.44 pounds of solid waste.(a) Does this mean every single American produces the same amount of garbage? What do you think this statement means?(b) Was the number 4 .44 obtained from a sample7
Cities must find better ways to dispose of solid waste. According to the Environmental Protection Agency, in a recent year, the composition of solid municipal waste was(a) Determine the percentage of other materials in the solid waste. This category includes glass, wood, rubber, and so on.(b)
Eighty customers at a bakery named their favorite pie. The responses are as follows:(a) Calculate the frequency for each pie.(b) Construct a pie chart. Pie Apple Pumpkin Pecan Other Frequency 31 28 12 9
The number of goals your favorite ice hockey team scores are to be collected for each game. These game totals are to b e grouped into the classes 0- 1, 2- 3, 4- 5, 7 or more. Both endpoints are included. Explain where a difficulty might arise.
Referring to Exercise 2.20, construct a density histogram using the intervals (6.5, 6.7 ], (6. 7, 6.9], (6.9, 7.1 ], ( 7.1, 7.5], and (7.5, 7.9 ].Using R: With the observations in xhist (x,breaks = c(6.5,6. 7,6.9, 7.1, 7.5, 7 .9), prob = T)Data from in Exercise 2.20In a recent year, 35 sites around
A sample of persons will each be asked to give the number of their close friends. The responses are to be grouped into the following classes: 0, 1-3, 3-5, 6 or more. Left endpoint is included. Explain where difficulties might arise.
Referring to Exercise 2.20, construct a five-stem display for the magnitude of earthquakes.Data from in Exercise 2.20In a recent year, 35 sites around the world experienced earthquakes of magnitude greater than 6.5.Construct a histogram using equal-length intervals starting with (6.5, 6.8 ], where
The weights of the players on the university football team (to the nearest pound) are to b e grouped into the following classes: 160-175, 175-190, 190-205, 205-220, 220-235, 235 or more. The left endpoint is included but not the right endpoint. Explain where difficulties might arise.
Calculate the mean and median for each of the following data sets.(a) 2 10 3 6 4(b) 3 2 7 4
Records show that in Las Vegas, NV, the normal daily maximum temperature (°F) for each month starting in January is56 62 68 77 87 99 105 102 95 82 66
In 2017, there were eight skyscrapers in the world over 500 meters tall. The ordered heights are508 530 541 555 594 601 632 828(a) Calculate the sample mean height for the eight skyscrapers.(b) Drop
On opening day one season, 10 major league baseball games were played and they lasted the following numbers of minutes.167 211 187 176 170 158 198 218 145 232Find the sample
For the data set6 2 4(a) Calculate the deviations (x - x̅) and check to see that they add up to 0.(b) Calculate the sample variance and the standard deviation.(c) Check your answers in Part b using software.R: x=c(6,2,4) then mean(x) and sd(x)
The mean and median salaries for middle management employees at two similar companies A and B in an area are as follows:
Rep eat (a) and (b) of Exercise 2.59 for the data set2.5 1.7 2.1 1.5 1.7Data from in Exercise 2.59For the data set 8 6 14 4(a) Calculate the deviations (x - x̅) and check to see that they add up to 0.(b) Calculate the
In 2017, there were eight skyscrapers in the world over 500 meters tall. The ordered heights are508 530 541 555 594 601 632 828(a) Calculate the sample variance for the eight skyscrapers.(b) Calculate
Find the standard deviation of the measurements of diameters given in Exercise 2.45.Data from in Exercise 2.45The following measurements of the diameters (in feet) of Indian mounds in southern Wisconsin were gathered by examining reports in the Wisconsin Archaeologist (courtesy of J. Williams).22
The performance time (minutes) for Beethoven's Ninth Symphony is obtained from each of seven compact discs.66.9 66.2 71.0 68.6 65.4 68.4 71.9(a) Find the sample median.(b) Find the sample mean.(c) Find the sample
The monthly number of hours students spend doing community service are summarized in the computer output:(a) Locate a measure of variation and also calculate the sample variance.(b) Calculate the interquartile range and interpret this value.(c) Give a value for the standard deviation that would
The weights ( oz) of nineteen babies born in Madison Wisconsin are summarized in the computer output.Obtain the z score for a baby weighing(a) 102 oz(b) 144 oz Descriptive Statistics: Weight Variable N Weight 19 118.05 117.00 Mean Median StDev 15.47
Two cities provided the following information on public school teachers' salaries.(a) Construct a boxplot for the salaries in City A.(b) Construct a boxplot, on the same graph, for the salaries in City B.(c) Are there larger differences at the lower or higher salary levels? Explain. Minimum Q₁
Referring to the earthquake data in Exercise 2.20,(a) Find the sample mean and standard deviation.(b) What proportion of these observations lies between x ± 2 s?Data from in Exercise 2.20In a recent year, 35 sites around the world experienced earthquakes of magnitude greater than 6.5.Construct a
Referring to the earthquake data in Exercise 2.20,(a) Obtain a five-number summary: minimum, Q1, Q2, Q3, maximum.(b) Construct a boxplot.Data from in Exercise 2.20In a recent year, 35 sites around the world experienced earthquakes of magnitude greater than 6.5.Construct a histogram using
The Dow Jones average provides an indication of overall market level. The changes in this average, (current year) - (previous year) summarize the year's activity. Changes for 48 recent years yield the following frequency table. The left-hand endpoint is excluded.(a) Calculate the relative frequency
With reference to the quit-smoking experiment, suppose two new subjects are available. Explain how you would assign one subject to receive the placebo and one to receive the medicated patch.
With reference to the quit -smoking experiment:(a) Suppose the placebo trials were ignored and you were only told that 120 of 216 were abstinent after using the medicated patches. Would this now appear to be stronger evidence in favor of the patches?(b) Explain why the placebo trials provide a more
For the data set(a) Construct a scatter diagram.(b) Guess the sign and value of the correlation coefficient.(c) Calculate the correlation coefficient. x у 1 5 3 3 6 1 4 4 1 2
A new study is widely reported to show that dog owners benefit by being more agreeable and extroverted than cat owners. Comment in light of facts that, on average, dogs cost more to maintain and that dog owners have larger incomes than cat owners.
If the value of r is small, can we conclude that there is not a strong relationship between the two variables?
(a) Construct scatter diagrams of the data sets(b) Calculate r for the data set (i).(c) Guess the value of r for the data set (ii) and then calculate r. (i) (ii) * } y y 1 4 3 5 2 5 1 7 1 4 2 7 1 4 5 3 3 4 ليا 3 5 لیا
Is the correlation in Figure 9 about (a) .1, (b) .5, (c) .9, or (d) –.7?Data from in Figure 9 y 10- 00 8 6- 4 T 2- 0 2 4 :. 6 - 00 8 Figure 9 Scatter diagram for Exercise 3.22. 10
The amount of municipal solid waste created has become a major problem. According to the Environmental Protection Agency, the yearly amounts (millions of tons) are:(a) Plot the amount of garbage ( millions of tons) versus year.(b) Visually, does there appear to be a strong correlation? Explain.(c)
The amount of municipal solid waste created has become a major problem. According to the Environmental Protection Agency, the yearly amounts (millions of tons) are:(a) Plot the amount of garbage (millions of tons) versus population (millions).(b) Fit a straight line using x = population in
Presidents also take midterms1 After two years of the president's term, members of Congress are up for election. The following table gives the number of net seats lost, by the party of the president, in the House of Representatives starting from Eisenhower's time.For the data on the number of House
Find x ands for the final times to run 1.5 miles in Table D.5 in the Data Bank.Data from in Table D.5 Data Bank TABLE D.5 Physical Fitness Improvement Pretest Posttest Pretest % Fat %
The mode of a collection of observations is defined as the observed value with largest relative frequency. The mode is sometimes used as a center value. There can be more than one mode in a data set. Find the mode for the checked bag data given in Exercise 2 .13.Data from in Exercise 2 .13A sample
Refer to the data on malt extract in Table D. 8 of the Data Bank.(a) Obtain sample mean and standard deviation.(b) Obtain quartiles.(c) Check conformity with the empirical rule.Data from in Table D. 8 Data Bank TABLE D.8 Malt
Given the following (x, y) values(a) Make a scatter plot.(b) Calculate r. X У 1 4 3 3 6 3 in 5 1 2 6 7 1
Refer to the data on garbage in Exercise 3.31.(a) Replace the year by (year - 1970). Calculate the correlation coefficient between (year - 1970) and amount of garbage in millions of tons.(b) Based on your calculation in part (a), what is the correlation between the year itself and the amount of
(a) Consider the simplistic model that human births are evenly distributed over the 12 calendar months. If a person is randomly selected, say, from a phone directory, what is the probability that his or her birthday would be in November or December?(b) The monthly number of births(thousands), in
Forest fires in the Western states are responsible for large losses. It was pointed out that the losses are greatest when many firefighters are present and least when there are only a few. Is this convincing evidence that losses can be cut by restricting the number of firefighters sent to battle
Birth rates in the 50 states, collected in a recent year by the Center for Health Statistics, are grouped into the following frequency table.Endpoint convention: Lower endpoint is included, upper endpoint is not.If one state is selected at random, what is the probability that the birth rate there
Identify the statement that best describes each P (A) .(a) P(A) = .04(b) P(A) = .36(c) P(A) = – .5 (i) P(A) is incorrect.(ii) A rarely occurs.(iii) A occurs moderately often.
Refer to Exercise 4.24. Using relative frequencies to estimate probabilities, find which 3 consecutive months have the lowest probability of a new birth.Data from in Exercise 4.24(a) Consider the simplistic model that human births are evenly distributed over the 12 calendar months. If a person is
Suppose S = { e1, e2, e3 }. If the simple events e1, e2, and e3 are all equally likely, what are the numerical values P( e1 ), P( e2 ) , and P( e3 )?
The probability of an event is often expressed in terms of odds. Specifically, when we say that the odds are k to m that an event will occur, we mean that the probability of the event is k / (k + m). For instance, "the odds are 4 to 1 that candidate Jones will win" means that P(Jones will win) =
A letter is chosen at random from the word "CHEERFUL." What is the probability that it is a vowel?
Friends will be called, one after another, and asked to go on a weekend trip with you. You will call until one agrees to go (A) or four friends are asked, whichever occurs first. List the sample space for the number of calls.
Campers arriving at a summer camp will be asked one after another whether they have protection against Lyme disease (Y) or not (N). The inspection will continue until one camper is found to be not protected or until five campers are checked, whichever occurs first. List the sample space for the
A random selection of 1000 smartphone owners, ages 18-24 years old, were asked if they constantly check and use their phone. A total of 518 responded yes.(a) Estimate the probability that, a smartphone owner in that age group constantly checks or uses his/her phone. Explain how you are using the
Suppose you have h ad interviews for summer jobs at a grocery store, a discount store, and a movie theater. Let G, D, and M denote the events of your getting an offer from the grocery store, the discount store, and the movie theater, respectively. Express the following events in set notation.(a)
If P(A) = .4 and P(B) = .7,can A and B be mutually exclusive? Why or why not?
A witness identified a suspect as having blond hair. However, when tested under lighting conditions similar to those on the night of the incident, it was concluded that the probability of correctly identifying blond hair is .80 and the probability of being incorrect about nonblond hair is .3.
Of three events, A, B, and C, suppose events A and B are independent and events B and C are mutually exclusive. Their probabilities are P(A) = .6, P(B) = .3, and P(C) = .2. Express the following events in set notation and calculate their probabilities.(a) Both B and C occur.(b) At least one of A
At one automated international airport arrival location, facial identification software compares a camera image of the traveler with a scan of their passport picture. The procedure correctly concludes a match with 99.4% of males and 98.8% of females. The other cases have to be handled by agents.(a)
A cable TV provider assigns 80% of its service calls to an independent contractor and 9% of these calls result in consumer complaints. The other 20% of the service calls are made by the companies' own employees, and these result in a 4% complaint rate. Find the(a) Probability of receiving a
A local company is giving away five streaming devices to persons who visit its website and register on a specified day. Each person is allowed to register three times for the drawing. If, at the time of drawing, there are 6200 entries, what is the probability that at least one of your three entries
A batch of 18 used automobile alternators contains 4 defectives. If 3 alternators are sampled at random, find the probability of the event(a) A = [None of the defectives appear](b) B = [Exactly two defectives appear ]
A college senior is selected at random from each state. Next, one senior is selected at random from the group of 50. Does this procedure produce a senior selected at random from those in the United States?
In one area city park, there are 15 trees, of which 9 are bushy and 6 that are not bushy. If 5 trees are selected at random to receive a new spray, what is the probability that exactly 3 bushy trees are selected?
Are the following methods of selection likely to produce a random sample of 5 students from your school? Explain.(a) Pick 5 students throwing flying discs on the mall.(b) Pick 5 students who are studying in the library on Friday night.(c) Select 5 students sitting near you in your statistics course.
Describe the sample space for each of the following experiments.(a) The number of different commercials shown next time you watch your favorite one-hour show.(b) The time your smartphone will last following an overnight charge.(c) A sample of 30 students are asked whether or not they visited a
For the experiments in Exercise 4.95, which sample spaces are discrete and which are continuous?Data from in Exercise 4.95Describe the sample space for each of the following experiments.(a) The number of different commercials shown next time you watch your favorite one-hour show.(b) The time your
A driver is stopped for erratic driving, and the alcohol content of his blood is checked. Specify the sample space and the event A = [level exceeds legal limit] if the legal limit is .10%.
Express the following statements in the notations of the event operations.(a) A occurs and B does not.(b) Neither A nor B occurs.(c) Exactly one of the events A and B occurs.
Suppose each of the numbers .2, .4, and .6 represents the probability of one of the events A, AB, and A ∪ B. Connect the probabilities to the appropriate events.
From the probabilities exhibited in this Venn diagram, findP(A̅), P(AB), P(B ∪ C), and P(BC). A .3 .1 .02 .18 .4 C B
Given P(AB) = .4 and P(B) = .5, find P(A I B).If, further, P(A) = .8, are A and B independent?

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