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elementary statistics

Just The Essentials Of Elementary Statistics 10th Edition Robert Johnson, Patricia Kuby - Solutions

14.20 A taste test was conducted with a regular beef pizza. Each of 133 individuals was given two pieces of pizza, one with a whole-wheat crust and the other with a white crust. Each person was then asked whether he or she preferred whole-wheat or white crust. The results were as follows:65
14.21 According to a local college’s NEWS website(http://www.cincynet.cnyric.org/Computers/Career/news"es.htm), 60% of high school seniors have mastered basic math—decimals, fractions, percentages, and simple equations. Suppose we wish to test the null hypothesis, “One-half of all seniors can
14.22 Fifty-one percent of grooms say they want to lose weight before their wedding day according to the June 30, 2005, USA Snapshot “Weigh-in before the wedding.” Suppose we wish to test the hypothesis that at least one-half of grooms want to lose weight before their wedding. If a random
14.23a. What parametric test procedure is comparable to the Mann–Whitney U test?b. What characteristic of the data used in a parametric test is not used in the Mann–Whitney U test?
14.24 Consider the side-by-side dotplots for the data values and for the ranks in Figure 14.2 on page 767. Do you see a different relationship between the two sets of data? Explain.
14.27 Determine the p-value that will result when testing the following hypotheses for experiments involving two independent samples:a. Ho: Average(A) Average(B)Ha: Average(A) Average(B)with nA 18, nB 15, and U 95.b. Ho: Average(I) Average(II)Ha: Average(I) Average(II)with nA 8, nB
14.28 Of the seven Mann–Whitney U test p-values given in Applied Example 14.8 on page 772, six are less than 0.001 and the seventh is 0.20. Explain how these p-values relate to statements containing phrases such as significant, drop dramatically, increased steadily, and did not change
14.29 Determine the critical value that would be used to test the following hypotheses for experiments involving two independent samples, using the classical method:a. Ho: Average(A) Average(B)Ha: Average(A) Average(B)with nA 18, nB 15, and 0.05.b. Ho: The average score is the same for
14.30 The Oregon Health & Science University’s news website (http://www.ohsu.edu/news/2003/071803smoke.html) gives information on a study that found that some commercial cigarette brands contained 10 to 20 times higher percentages of nicotine in the “free-base” form, that is, the form thought
14.31 [EX14-31] Pulse rates were recorded for 16 men and 13 women. The results are shown in the following table.These data were used to test the hypothesis that the distribution of pulse rates differs for men and women. The following MINITAB output printed out the sum of ranks for males (W 192.0)
14.32 [EX14-32] The Ohio State Proficiency test results for Toledo, Ohio, fourth-grade students was the highest recorded since the start of the statewide proficiency testing. Although the results were an improvement districtwide, in some subjects there was not as much improvement as for other
14.33 A study titled “Factors Leading to Reduced Intraocular Pressure after Combined Trabeculotomy and Cataract Surgery” in the Journal of Glaucoma (http://www.glaucomajournal.com/pt/re/jglaucoma/abstract) investigated the influence cataract surgery alone and cataract surgery with trabeculotomy
14.34 [EX14-34] An article in the International Journal of Sports Medicine discusses the use of the Mann–Whitney U test to compare the total cholesterol(mg/dL) of 35 adipose (obese) boys with that of 27 adipose girls. No significant difference was found between the two groups with respect to
14.35 [EX14-35] As part of a study to determine whether cloud seeding increased rainfall, clouds were randomly seeded or not seeded with silver nitrate. The amounts of rainfall that followed are listed here.Do these data show that cloud seeding will significantly increase the average amount of
14.36 [EX14-36] Fifteen Texas and eleven Oklahoma peanut-producing counties were randomly identified, and the 2004 peanut yield rate, in pounds of peanuts harvested per acre, was recorded.Use the Mann–Whitney U statistic to test the hypothesis that the average yield is different for the two
14.40 Jessica did not believe she was playing a game with a fair die. She thought that if the die was fair, the tossing of the die should result in a random order of even and odd output. She performed her experiment 14 times. After each toss, Jessica recorded the results. The following data were
14.41 A manufacturing firm hires both men and women. The following shows the gender of the last 20 individuals hired (M male, F female).M M F M F F M M M M M M F M M F M M M M At the 0.05 level of significance, are we correct in concluding that this sequence is not random?
14.42 In an attempt to answer the question, “Does the husband (h) or wife (w) do the family banking?”the results of a sample of 28 married customers doing the family banking show the following sequence of arrivals at the bank.w w w w h w h h h h w w w w w h h w w w h h h h w h h w Do these data
14.43 [EX14-43] The following data were collected in an attempt to show that the number of minutes the city bus is late is steadily growing larger. The data are in order of occurrence.Minutes: 6 1 3 9 10 10 2 5 5 6 12 3 7 8 9 4 5 8 11 14 At 0.05, do these data show sufficient lack of randomness
14.44 A student was asked to perform an experiment that involved tossing a coin 25 times. After each toss, the student recorded the results. The following data were reported (H heads, T tails).H T H T H T H T H H T T H H T T H T H T H T H T H Use the runs test at a 5% level of significance to
14.45 [EX14-45] According to a new survey—the Information and Communications Technologies in Schools Survey (http://www.statcan.ca/Daily/English/040610/d040610b.htm)—virtually all elementary and secondary schools in Canada had computers and were connected to the Internet during the 2003–2004
14.46 [EX14-46] According to the March 10, 2005, USA Today article titled “Electronic world swallows up kids’ time, study finds,” U.S. children are spending an average of approximately 6.5 hours a day watching television, using the computer, or enjoying other electronic activities. The
[EX14-47] The following are 24 consecutive downtimes (in minutes) of a particular machine.Downtime: 20 33 33 35 36 36 22 22 25 27 30 30 30 31 31 32 32 36 40 40 50 45 45 40 The null hypothesis of randomness is to be tested against the alternative that there is a trend. A MINITAB analysis of the
14.48 Posted on the Economic Statistics Briefing Room page of the White House’s website on June 20, 2005, was the statement, “Median household income in 2002 in the United States was $42,409.”A random sample of 250 incomes has a median value different from any of the 250 incomes in the
14.49 [EX14-49] The number of absences recorded at a lecture that met at 8 AM on Mondays and Thursdays last semester were (in order of occurrence)n(absences) 5 16 6 9 18 11 16 21 14 17 12 14 10 6 8 12 13 4 5 5 6 1 7 18 26 6 Do these data show a randomness about the median value at 0.05?
14.50 [EX14-50] The students in a statistics class were asked if they could be a good randomnumber generator. Each student was asked to write down a single digit from 0 through 9. The data was collected starting at the front left of the class, moving row by row, to the back right of the class. The
14.52 Research Randomizer is a free service offered to students and researchers interested in conducting random assignment and random sampling.Although every effort has been made to develop a useful means of generating random numbers, Research Randomizer and its staff do not guarantee the quality
14.55 Determine the test criteria that would be used to test the null hypothesis for the following Spearman rank correlation experiments:a. Ho: No relationship between the two variables.Ha: There is a relationship.with n 14 and 0.05.b. Ho: No correlation Ha: Positively correlated with n 27
14.56 [EX14-56] When it comes to getting workers to produce, money is not everything; feeling appreciated is more important. Do the rankings assigned by workers and the boss show a significant difference in what each person thinks is important?(Ratings: 1 most important; 10 least important.)Test
14.58 [EX14-58] Reader’s Digest (July 2005) did a special report on “America’s Cleanest [and Dirtiest]Cities.” The 50 most populous U.S. cities were compared and ranked based on air pollution, water pollution, toxic emissions, hazardous waste, and sanitation force. The top 10 cleanest
14.59 [EX14-59] The following data represent the ages of 12 subjects and the mineral concentration(in parts per million) in their tissue samples. Age, x 82 83 64 53 47 50 70 62 34 27 75 28 Mineral Concentration, y 170 40 64 5 15 5 48 34 3 7 50 10 Refer to the following MINITAB output and verify
The Journal of Professional Nursing article titled “The Graduate Record Examination as an Admission Requirement for the Graduate Nursing Program” reported a significant correlation between undergraduate grade point average (GPA) and GPA at graduation from a graduate nursing program. The
The U.S. Department of Transportation tracks and reports a variety of information regarding airlines and airports. It reports the“percent on-time” frequently. Compare the percent on-time for the 33 major airports in the United States for the 4 months of 2004 and 2005.At the 0.05 level of
Most people in the United States work in either trade or service jobs. “Trade” is defined as businesses such as retail stores, car dealers, and restaurants—places where goods are sold. The“service” area includes jobs such as those in health care, the hotel industry, and cleaning
“Survey of Home Buyer Preferences”was conducted by the National Association of Home Builders to determine the features that home buyers really want. Respondents were to rate each feature desirable as well as if essential.The following table shows the results.Feature Desirable Essential Laundry
14.65 [EX14-65] As the following chart shows, what is “good enough” to qualify as “proficient”may vary widely from state to state. Education Week(February 20, 2002) compared the percent of students who scored at or above proficient on the National Assessment of Educational Progress
14.67 Using formula (3.2), calculate the Spearman rank correlation coefficient for the data in Example
14.14 (p. 787). Recall that formula (3.2) is equivalent to the definition formula (3.1) and that rank numbers must be used with this formula for the resulting statistic to be the Spearman rs.
14.70 [EX14-70] Research about the health practices of cardiovascular technologists compared the body mass index (BMI) of the technologists with that of the general population. Weight classification by BMI is as follows: underweight, less than 19; normal, 19 to 24; overweight, 25 to 29; and
14.71 [EX14-71] A sample of 32 students received the following grades on an exam.41 42 48 46 50 54 51 42 51 50 45 42 32 45 43 56 55 47 45 51 60 44 57 57 47 28 41 42 54 48 47 32a. Does this sample show that the median score for the exam differs from 50? Use 0.05.b. Does this sample show that the
14.72 [EX14-72] Is the absentee rate in the 8 AM statistics class the same as that in the 11 AM statistics class? The following sample of the daily number of absences was taken from the attendance records of the two classes.Is there sufficient reason to conclude that there are more absences in the
14.73 [EX14-73] Track coaches, runners, and fans talk a lot about the “speed of the track.” The surface of the track is believed to have a direct effect on the amount of time that it takes a runner to cover the required distance. To test this effect, 10 runners were asked to run a 220-yard
An article in the journal Sedimentary Geology compares a measure called the roughness coefficient for translucent and opaque quartz sand grains. If you measured the roughness coefficient for 20 sand grains of each type (translucent and opaque), for what values of the Mann–Whitney U statistic
Twenty students were randomly divided into two equal groups. Group 1 was taught an anatomy course using a standard lecture approach.Group 2 was taught using a computer-assisted approach. The test scores on a comprehensive final exam were as follows:Group 1 75 83 60 89 77 92 88 90 55 70 Group 2 77
Two statistics that baseball enthusiasts use to compare the overall strengths of one team against another are team batting average(the higher the batting average, the better) and team pitching average (the lower the earned run average, the better). Using the results for the National and American
Consider the following sequence of defective parts (d) and nondefective parts (n) produced by a machine.n n n d n n n n n d n n n n n n n d n d n n n n Can we reject the hypothesis of randomness at 0.05?
[EX14-82] A patient was given two different types of vitamin pills, one that contained iron and one that did not contain iron. The patient was instructed to take the pills on alternate days. To avoid having to remember which pill to take on a particular day, the patient mixed all of the pills
14.83 [EX14-83] What makes one company more attractive to work for than another? One possibility is the growth in new jobs. The editors of Fortune developed a list of the top 100 companies to work for in America. Included in the list was the percentage change in full-time positions of each company
14.84 [EX14-84] In a study to see whether spouses are consistent in their preferences for television programs, a market research firm asked several married couples to rank a list of 12 programs(1 represents the highest score; 12 represents the lowest). The average ranks for the programs, rounded to
14.85 [EX14-85] Can today’s high temperature be effectively predicted using yesterday’s high? Pairs of yesterday’s and today’s high temperatures were randomly selected. The results are shown in the following table. Do the data present sufficient evidence to justify the statement:
14.86 [EX14-86] U.S. commercial radio stations are classified by the primary format of their broadcasts.As people change their listening preferences, the stations are likely to react to the change by adjusting their formats. The following table shows the percentages of radio stations in 1997, 2002,
14.87 [EX14-87] Every year before the college football season starts, Sports Illustrated presents its college football preview and ranks the top 25 teams based primarily on scouting reports. As the season progresses, other college football polls provide a weekly ranking of the teams, evaluations
14.89a. Do responses from the boys and the girls have the same distribution? Use the Mann–Whitney U test and 0.05.b. Rank the choices for the boys and girls separately of each other.c. Do the boys’ preferences correlate to the girls’ preferences? Use Spearman’s rank correlation to test at
Define a population of your choice and randomly sample the following variables:Variable 1: Gender or class level (freshmen, sophomore, upper classes, etc.)Variable 2: Name “The One Thing Want Most From Life”; choose from happiness, long enjoyable life, marriage and family, financial success,
One of the advantages of the nonparametric tests is the necessity for less restrictive assumptions. True/false
The sign test is a possible replacement for the F-test. True/false
The sign test can be used to test the randomness of a set of data. True/false
If a tie occurs in a set of ranked data, the data that form the tie are removed from the set. True/false
Two dependent means can be compared nonparametrically by using the sign test. True/false
The sign test is a possible alternative to Student’s t-test for one mean value. True/false
The runs test is a nonparametric alternative to the difference between two independent means. True/false
The confidence level of a statistical hypothesis test is measured by 1 . True/false
Spearman’s rank correlation coefficient is an alternative to using the linear correlation coefficient. True/false
The efficiency of a nonparametric test is the probability that a false null hypothesis is rejected. True/false
The weights (in pounds) of nine people before they stopped smoking and five weeks after they stopped smoking are listed here: [PT14-11]Find the 95% confidence interval estimate for the average weight change. Person 1 2 3 4 5 6 7 8 9 Before 148 176 153 116 128 129 120 132 154 After 155 178 151 120
The following data show the weight gains(in ounces) for 20 laboratory mice, half of which were fed one diet and half a different diet. Test to determine whether the difference in weight gain is significant at 0.05. [PT14-12] Diet A 41 40 36 43 36 43 39 36 24 41 Diet B 35 34 27 39 31 41 37 34 42 38
A large textbook publishing company hired nine new sales representatives 3 years ago. At the time of hire, the nine were ranked according to their potential.Now 3 years later the company president wants to know how well their potential ranks correlate with their sales totals for the 3 years.
The new school principal thought there might be a pattern to the order in which discipline problems arrived at his office. He had his secretary record the grade levels of the students as they arrived. [PT14-14]At the 0.05 level, is there significant evidence of randomness? 9 10 11 9 12 11 9 10 10
What advantages do nonparametric statistics have over parametric methods?
Explain how the sign test is based on the binomial distribution and is often approximated by the normal distribution.
Why does the sign test use a null hypothesis about the median instead of the mean like a t-test uses?
Explain why a nonparametric test is not as sensitive to extreme data as a parametric test might be.
A restaurant has collected data on which of two seating arrangements its customers prefer. In a sign test to determine whether one seating arrangement is significantly preferred, which null hypothesis would be used?a. M 0b. M 0.5c. p 0d. p 0.5 Explain your choice.
Discuss why age should be used instead of manufacture year. Asking Asking Asking Asking Asking Year Price Year Price Year Price Year Price Year Price 2001 $35,800 1989 $15,700 1989 $18,200 1998 $26,500 1995 $18,900 1995 $19,900 2002 $35,500 1992 $17,900 2001 $36,000 2000 $33,000 1996 $26,700 2001
Convert manufacture year to the variable age, x, using the preceding formula. Asking Asking Asking Asking Asking Year Price Year Price Year Price Year Price Year Price 2001 $35,800 1989 $15,700 1989 $18,200 1998 $26,500 1995 $18,900 1995 $19,900 2002 $35,500 1992 $17,900 2001 $36,000 2000 $33,000
Construct side-by-side vertical dotplots of theasking price for each year of age. Asking Asking Asking Asking Asking Year Price Year Price Year Price Year Price Year Price 2001 $35,800 1989 $15,700 1989 $18,200 1998 $26,500 1995 $18,900 1995 $19,900 2002 $35,500 1992 $17,900 2001 $36,000 2000
Does it appear that the asking price for aCorvette is affected by its age? Describe the effectas pictured on the graph shown for question3. Asking Asking Asking Asking Asking Year Price Year Price Year Price Year Price Year Price 2001 $35,800 1989 $15,700 1989 $18,200 1998 $26,500 1995 $18,900 1995
Complete a one-way ANOVA and test the hypothesis that age has no effect on the asking price. Use 0.05. Asking Asking Asking Asking Asking Year Price Year Price Year Price Year Price Year Price 2001 $35,800 1989 $15,700 1989 $18,200 1998 $26,500 1995 $18,900 1995 $19,900 2002 $35,500 1992 $17,900
What effect would using year of manufacture instead of age have on the above analysis? Asking Asking Asking Asking Asking Year Price Year Price Year Price Year Price Year Price 2001 $35,800 1989 $15,700 1989 $18,200 1998 $26,500 1995 $18,900 1995 $19,900 2002 $35,500 1992 $17,900 2001 $36,000 2000
Discuss why using age instead of manufacture year results in a scatter diagram that is more representative of behavior of the price or value of a used car as it ages. Describe how a scatter diagram using year of manufacture as x would differ from one using age as x. Asking Asking Asking Asking
Construct and label a scatter diagram of Peggy’s data. Asking Asking Asking Asking Asking Year Price Year Price Year Price Year Price Year Price 2001 $35,800 1989 $15,700 1989 $18,200 1998 $26,500 1995 $18,900 1995 $19,900 2002 $35,500 1992 $17,900 2001 $36,000 2000 $33,000 1996 $26,700 2001
Discuss the relationship between the side-byside dotplots drawn in question 3 and the scatter diagram drawn in question 8. Asking Asking Asking Asking Asking Year Price Year Price Year Price Year Price Year Price 2001 $35,800 1989 $15,700 1989 $18,200 1998 $26,500 1995 $18,900 1995 $19,900 2002
Determine the equation for the line of best fit. Asking Asking Asking Asking Asking Year Price Year Price Year Price Year Price Year Price 2001 $35,800 1989 $15,700 1989 $18,200 1998 $26,500 1995 $18,900 1995 $19,900 2002 $35,500 1992 $17,900 2001 $36,000 2000 $33,000 1996 $26,700 2001 $35,700 2002
Draw the line of best fit on the scatter diagram. Asking Asking Asking Asking Asking Year Price Year Price Year Price Year Price Year Price 2001 $35,800 1989 $15,700 1989 $18,200 1998 $26,500 1995 $18,900 1995 $19,900 2002 $35,500 1992 $17,900 2001 $36,000 2000 $33,000 1996 $26,700 2001 $35,700
Test the question of the line of best fit to see whether the linear model is appropriate for the data. Use 0.05. Asking Asking Asking Asking Asking Year Price Year Price Year Price Year Price Year Price 2001 $35,800 1989 $15,700 1989 $18,200 1998 $26,500 1995 $18,900 1995 $19,900 2002 $35,500
Construct a 95% confidence interval for the mean advertised price for 1994 Corvettes. Asking Asking Asking Asking Asking Year Price Year Price Year Price Year Price Year Price 2001 $35,800 1989 $15,700 1989 $18,200 1998 $26,500 1995 $18,900 1995 $19,900 2002 $35,500 1992 $17,900 2001 $36,000 2000
Draw a line segment on the scatter diagram that represents the interval estimate found for question 13. Asking Asking Asking Asking Asking Year Price Year Price Year Price Year Price Year Price 2001 $35,800 1989 $15,700 1989 $18,200 1998 $26,500 1995 $18,900 1995 $19,900 2002 $35,500 1992 $17,900
What does the value of the slope, b1, represent?Explain. Asking Asking Asking Asking Asking Year Price Year Price Year Price Year Price Year Price 2001 $35,800 1989 $15,700 1989 $18,200 1998 $26,500 1995 $18,900 1995 $19,900 2002 $35,500 1992 $17,900 2001 $36,000 2000 $33,000 1996 $26,700 2001
What does the value of the y-intercept, b0, represent?Explain. Asking Asking Asking Asking Asking Year Price Year Price Year Price Year Price Year Price 2001 $35,800 1989 $15,700 1989 $18,200 1998 $26,500 1995 $18,900 1995 $19,900 2002 $35,500 1992 $17,900 2001 $36,000 2000 $33,000 1996 $26,700
Write a meaningful paragraph answering the general questions of concern:a. Is the effect of age on price predictable?b. Can a meaningful relationship between the age and the typical asking price for used Corvettes be established?c. What is an average asking price for a 1994 Corvette that is for
Define the population, the independent variable, the dependent variable, and the purpose for studying these two variables as a regression analysis.
Collect 15 to 20 ordered pairs of data.
Partition the independent variable values into three or more categories that are meaningful or appropriate for your data.
Complete a one-way ANOVA and test the hypothesis that the independent variable has no effect on the dependent variable.
Construct and label a scatter diagram of your data.
Determine the equation for the line of best fit.
Draw the line of best fit on the scatter diagram.
8. Test the equation of the line of best fit to see whether the linear model is appropriate for the data. Use 0.05.
9. Construct a 95% confidence interval for the mean value of the dependent variable at the following value of x: Let x be equal to onethird the sum of the lowest value of x in your sample and twice the largest value; that is, x L 3 2H
10. Draw a line segment on the scatter diagram that represents the interval estimate found for question 9.

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