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mathematics
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Statistics For Management And Economics Abbreviated 10th Edition Gerald Keller - Solutions

Of the seven Mann–Whitney U test p-values given in Applied Example 14. 8 on page 684, 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 significantly.
Given the following data from group 1 and group 2:a. Combine the two datasets in ranked order. Compute the sum of the ranks for group 1, R1. Compute the sum of the ranks for group 2, R2. b. Compute the U score for each group, U1 and U2, and determine the U_ statistic. c. Use the
The following daily high temperatures (°F) were recorded in the city of Rochester, New York, on 20 randomly selected days in December.Use the sign test to determine the 95% confidence interval for the median daily high temperature in Rochester, New York, during December.
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 total
A study titled €œFactors Leading to Reduced Intraocular Pressure after Combined Trabeculotomy and Cataract Surgery€ in the Journal of Glaucoma (www. glaucomajournal.) investigated the influence cataract surgery alone and cataract surgery with trabeculotomy has on eye pressure.
Ten North Carolina and 13 Texas peanut-producing counties were randomly identified and the 2008 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 states. Use a =
The Oregon Health & Science University’s news website (www.ohsu.edu) gives information on a study that found that some commercial cigarette brands contain 10 to 20 times higher percentages of nicotine in the “free-base” form, that is, the form thought to be the most addictive. Consider
As part of a study to determine whether cloud seeding increased rainfall, clouds were randomly seeded with silver nitrate or not seeded. The amounts of rainfall that followed are listed here.Do these data show that cloud seeding significantly increases the average amount of rainfall? Use a = 0.05
Are more hours spent watching sporting events on television or reality shows? A community college student hypothesized that males more likely watch sports whereas females watch the reality shows. With this premise, he randomly gathered data from 30 males and 30 females at his community college on
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test the following statements: a. The data did not occur in a random order about the median. b. The sequence of odd and even is not random. c. The gender of customers entering a grocery store was recorded; the
Determine the p-value that would be used to complete the following runs tests: a. Ho: The sequence of gender of customers coming into the gym was random; Ha: The sequence was not random; with n(A) = 10, n(B) = 12, and V = 5. b. Ho: The home prices collected occurred in random order above and below
Determine the critical values that would be used to complete the following runs tests using the classical approach: a. Ho: The results collected occurred in random order above and below the median; Ha: The results were not random; with n(A) = 14 n(B) = 15 and a = 0.05. b. Ho: The two properties
Fifteen Georgia peanut-producing counties were randomly identified, and the 2008 peanut-yield rate, in pounds of peanuts harvested per acre, was recorded.Use the sign test to determine the 95% confidence interval for the median yield rate for peanuts.
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 result. The following data were reported
A manufacturing firm hires both men and women. The following shows the gender of the last 20 individuals Hired (M = male F = female)At the a = 0.05 level of significance, are we correct in concluding that this sequence is not random?
In an attempt to answer the question, €œDoes 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.Do these data show lack of randomness with regard to
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)Use the runs test at a 5% level of significance to test the student€™s claim that the results
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.At a = 0.05 do these data show sufficient lack of randomness to support the claim?
According to a new survey from the Boston Indicator.org website, Boston city schools had an average of 3.6 students per computer for the 2007€“2008 school year. The average was the same for the whole state of Massachusetts but higher than the average for any of the suburban districts. A
On June 24, 2009, the 2008 American Time Use Survey was released by the Bureau of Labor Statistics. Among the many statistics provided was information on leisure-type activities and the average amount of time spent on various categories. For 15- to 19-yearolds, the average time spent playing games
The following are 24 consecutive downtimes (in minutes) of a particular machine.The null hypothesis of randomness is to be tested against the alternative that there is a trend. A MINITAB analysis of the number of runs above and below the median follows. a. Confirm the values reported for the
According to an August 26, 2008, press release from the U.S. Census Bureau News, the median household income in 2007 was $50,023. A random sample of 250 incomes has a median value different from that of any of the 250 incomes in the sample. The data contain 105 runs above and below the median. Use
The number of absences recorded from a lecture that met at 8 a.m. on Mondays and Thursdays last semester were (in order of occurrence)Do these data show a randomness about the median value at a = 0.05 ? Complete this test by using (a) critical values from Table 14 in Appendix B and (b) the standard
Every year sixth-grade students in Ohio schools take proficiency tests. The following list is of sixth-grade reading score changes from the prior year. Negative values indicate a decrease in score, positive values show an increase, and a zero shows no change from the prior year.Construct a 95%
The students in a statistics class were asked if they could be a good random number generator. Each student was asked to write down a single digit from 0 through 9. The data were collected starting at the front left of the class, moving row by row, to the back right of the class. The sequence of
Randomness incorporates many different concepts. Referring to Applied Example 14. 12: a. What aspect of randomness will be tested using the chi-square test mentioned in part (i) of rule (c)? Describe how it will be used. b. What aspect of randomness will be tested using the runs test mentioned in
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 or
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test the following statements: a. There is no relationship between the two rankings. b. The two variables are unrelated. c. There is a positive correlation between the two variables. d. Refrigerator age has a
Determine the p-value 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 positive relationship; With n = 21 and rs = 0.55 b. Ho: No correlation; Ha:There is a relationship; with n
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 a = 0.05. b. Ho: No correlation; Ha: Positively correlated; with n = 27
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 using a =
Consumer product testing groups commonly supply ratings of all sorts of products to consumers in an effort to assist them in their purchase decisions. Different manufacturers€™ products are usually tested for their performance and then given an overall rating. PC World ranked the top ten
What can you do with a two-year degree from a community college? Consider the information taken from the September 2, 2009, USA Today article titled €œHealth care, energy among €˜hot€™ jobs.€a. Rank the percentage growth and median incomes in ascending order
The following data represent the ages of 12 subjects and the mineral concentration (in parts per million) in their tissue samples.
A sample of the daily rental-car rates for a compact car was collected in order to estimate the average daily cost of renting a compact car. (See data below.) Find the 99% confidence interval for the median daily rental cost.
Many people are concerned about eating foods that have a high sodium content. They are also advised of the benefits of obtaining sufficient fiber in their diets. Do foods high in fiber tend to have more sodium? The following table was obtained by selecting 11 soups from a list published in
The Journal of Professional Nursing article titled €œThe 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
The U.S. Department of Transportation tracks and reports a wide variety of information regarding airlines and airports. It reports the €œpercent on-time€ frequently. Compare the percent on-time arrival performance for the 31 major airports in the United States for the year to
The November 24, 2009, USA Today article €œFlier satisfaction with airlines goes up a bit€ reported the results from a Zagat Survey of 5900 fliers who averaged 17 flights a year. The survey had fliers rate airlines using a 30-point scale. The airline ratings for coach
A €œSurvey 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 which features were desirable and/or essential. The following table shows the results.It is not
As the following chart shows, what is €œgood enough€ to qualify as €œproficient€ may vary widely from state to state. Education Week compared the percent of students who scored at or above proficient on the National Assessment of Educational Progress (NAEP)
Referring to Applied Example 14. 15: a. Explain the meaning of “the mean scores are significantly different (p = 0.0001) What mean scores are being referred to? What methodology might have been used to establish this significance? b. Explain the meaning of “Pearson correlation analysis shows
Using formula (3.2), calculate the Spearman rank correlation coefficient for the data in Example 14. 14 (p. 697).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.
Refer to the bivariate data shown in the following table.a. Construct a scatter diagram. b. Calculate the Spearman rank correlation coefficient, rs [formula (14.11)]. c. Calculate Pearson€™s correlation coefficient, r [formula (3.2)]. d. Compare the two results from parts b and c. Do the
€œBecause regional-scale atmospheric deposition data in the Rocky Mountains are sparse, a program was designed by the U.S. Geological Survey to more thoroughly determine the quality of precipitation and to identify sources of atmospherically deposited pollution in a network of
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test the following statements: a. The median length of vacation time is less than 18 days. b. The median value is at least 32. c. The median tax rate is 4.5%.
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 obesity, 30 and higher.
A sample of 32 students received the following grades on an exam.a. Does this sample show that the median score for the exam differs from 50? Use a = 0.05 b. Does this sample show that the median score for the exam is less than 50? Use a = 0.05.
Is the absentee rate in the 8 a.m. statistics class the same as that in the 11 a.m. 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 8 a.m.
Track coaches, runners, and fans talk a lot about the €œspeed 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
A candy company has developed two new chocolate- covered candy bars. Six randomly selected people all preferred candy bar I. Is this statistical evidence, at a = 0.05, that the general public will prefer candy bar I?
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:Test the claim that a computer-assisted approach
The use of nuclear magnetic resonance (NMR) spectroscopy for detection of malignancy is discussed in the journal Clinical Chemistry. The line width at the half height of peaks in the NMR spectrum is measured. The spectrum is produced from assaying plasma from an individual. Suppose the following
A firm is currently testing two different procedures for adjusting the cutting machines used in the production of greeting cards. The results of two samples show the following recorded adjustment times (in seconds).Is there sufficient reason to conclude that method 2 requires less time, on average,
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
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test the following statements. a. Post–self-esteem survey scores were higher than pre–self-esteem survey scores. b. People prefer the taste of the bread made with the new recipe. c. There is no change in
Two manufacturers of table-tennis balls have agreed that the quality of their products can be measured by the height to which the balls rebound. A test is arranged, the balls are dropped from a constant height, and the rebound heights are measured. The results (in inches) are shown in the following
Consider the following sequence of defective parts (d) and nondefective parts (n) produced by a machine.Can we reject the hypothesis of randomness at a = 0.05 ?
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 together in a
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 the nearest
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 “Today’s high
Nonparametric tests are also called distributionfree tests. However, the normal distributions are used in the inference-making procedures. a. To what does the distribution-free term apply? (The population? The sample? The sampling distribution?) Explain. b. What is it that has the normal
Determine the p-value for the following hypothesis tests involving the sign test:
Find the probabilities.P(Z < – 2.30)
Refer to exercise 8.6. The professor wants to reward (with bonus marks) students who are in the lowest quarter of completion times. What completion time should he use for the cutoff for awarding bonus marks?
Refer to exercise 8.6. The professor would like to track (and possibly help) students who are in the top 10% of completion times. What completion time should he use?
Find the probabilities. P (Z < 1.50)
Find the probabilities. P(Z < 1.51)
Find the probabilities. P (Z < 1.55)
Find the probabilities. P (Z < – 1.59)
Find the probabilities. P(Z < – 1.60)
Find the probabilities. P(Z < 2.84)
Find the probabilities. P(Z > –1.44)
Find the probabilities. P(Z < 2.03)
Find the probabilities. P(Z > 1.67)
Find the probabilities. P(Z > 0)
Find the probabilities. P(Z > 3.09)
Describe what happens to the expected value and standard deviation of the portfolio returns when the coefficient of correlation decreases.
Let X be the random variable designating the number of spots that turn up when a balanced die is rolled. What is the probability distribution of X?
Second-year business students at many universities are required to take 10 one-semester courses. The number of courses that result in a grade of A is a discrete random variable. Suppose that each value of this random variable has the same probability. Determine the probability distribution.
A gambler believes that a strategy called "doubling up" is an effective way to gamble. The method requires the gambler, to double the stake after each loss. Thus, if the initial bet is $1, after losing he will double the bet until he wins. After a win, he resorts back to a $1 bet. The result is
You have been given the choice of receiving $500 in cash or receiving a gold coin that has a face value of $100. However, the actual value of the gold coin depends on its gold content. You are told that the coin has a 40% probability of being worth $400, a 30% probability of being worth $900, and
The owner of a small firm has just purchased a personal computer, which she expects will serve her for the next 2 years. The owner has been told that she "must" buy a surge suppressor to provide protection for her new hardware against possible surges or variations in the electrical current, which
To examine the effectiveness of its four annual advertising promotions, a mail-order company has sent a questionnaire to each of its customers, asking how many of the previous year's promotions prompted orders that would not otherwise have been made. The table lists the probabilities that were
Refer to Exercise 7.40. A previous analysis of historical records found that the mean value of orders for promotional goods is $20, with the company earning a gross profit of 20% on each order. Calculate the expected value of the profit contribution next year.
Refer to Exercises 7.40 and 7.41. The fixed cost of conducting the four promotions is estimated to be $15,000, with a variable cost of $3.00 per customer for mailing and handling costs. How large a customer base does the company need to cover the cost of promotions?
A statistics practitioner working for major league baseball determined the probability that the hitter will be out on ground balls is .75. In a game where there are 20 ground balls, find the probability that all of them were outs.The following exercises are best solved with a computer.
The leading brand of dishwasher detergent has a 30% market share. A sample of 25 dishwasher detergent customers was taken. What is the probability that 10 or fewer customers chose the leading brand?
According to the American Academy of Cosmetic Dentistry, 75% of adults believe that an unattractive smile hurts career success. Suppose that 25 adults are randomly selected. What is the probability that 15 or more of them would agree with the claim?
A student majoring in accounting s trying to decide on the number of firms to which he should apply. Given his work experience and grades, he can expect to receive a job offer from 70% of the firms to which he applies. The student decides to apply to only four firms. What is the probability that he
Most dial-up Internet service providers (ISPs) attempt to provide a large enough service so that customers seldom encounter a busy signal. Suppose that the customers of one ISP encounter busy signals 8% of the time. During the week, a customer of this ISP called 25 times. What is the probability
Major software manufacturers offer a help line that allows customers to call and receive assistance in solving their problems. However, because of the volume of calls, customers frequently are put on hold. One software manufacturer claims that only 20% of callers are put on hold. Suppose that 100
Perform the Durbin-Watson test at the 5% significance level to determine whether positive first-order autocorrelation exists when d = 1.10, n = 25, and k = 3.
Determine whether negative first-order autocorrelation exists when d = 2.85, n = 50, and k= 5. (Use a 1% significance level.)
Given the following information, perform the Durbin-Watson test to determine whether first-order autocorrelation exists:n = 25,k = 5, α = .10,d = .90
Test the following hypotheses with α = .05. Ho: There is no first-order autocorrelation HI: There is positive first-order autocorrelation n = 50, k = 2, d = 1.38
Test the following hypotheses with α = .02.Ho: There is no first-order autocorrelationHI: There is first-order autocorrelationn = 90, k = 5, d = 1.60
Test the following hypotheses with α = .05.Ho: There is no first-order autocorrelationHi: There is negative first-order autocorrelationn = 33, k = 4,d =2.25
Is the sample median an unbiased estimator of the population mean? Explain.
How do point estimators and interval estimators differ?

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