Speed Dating In a study of speed dating conducted at Columbia University, female subjects were asked to rate the attractiveness of their male dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive). Use the sign test to test the claim t...
31 May 2021California Lottery Listed below are consecutive first-digits drawn in the California Daily 4 lottery. Test for randomness of even and odd integers. Does the lottery appear to be working as it should? 5 2 2 8 4 8 8 7 1 0 6 4 1 5 1 5 ...
31 May 2021World Series The last 110 baseball World Series ended with 63 wins by American League teams and 47 wins by National League teams. Use the sign test to test the claim that in each World Series, the American League team has a 0.5 probability of winning.
31 May 2021Presidents, Popes, Monarchs Listed below are numbers of years that U.S. presidents, popes, and British monarchs lived after their inauguration, election, or coronation, respectively. Assume that the data are samples randomly selected from larger populations. Test the claim that...
31 May 2021Job Stress and Income Listed below are job stress scores and median annual salaries (thousands of dollars) for various jobs, including firefighters, airline pilots, police officers, and university professors (based on data from “Job Rated Stress Score” from CareerCast.com). Do th...
31 May 2021Which Test? Three different judges give the same singers ratings on a scale of 0 to 10. What method of this chapter can be used to determine whether one of the judges is tougher or more lenient than the others, as indicated by a median rating that is significantly different from ...
31 May 2021Sign Test and Wilcoxon Signed-Ranks Test What is a major advantage of the Wilcoxon signed-ranks test over the sign test when analyzing data consisting of matched pairs?
31 May 2021Runs Test Consider sample data consisting of genders of criminals charged with hacking computer systems of corporations. Determine whether the following are true or false. a. If the runs test suggests that sample data occur in a random order, then it follows that the data have b...
31 May 2021Runs Test Assume that we use the runs test of randomness above and below the mean for the monetary value of Google at the end of each year for 20 years and we find that G = 2. What does that value tell us about the monetary value of Google?
31 May 2021Nonparametric Tests a. Which of the following terms is sometimes used instead of “nonparametric test”: normality test; abnormality test; distribution-free test; last testament; test of patience? b. Why is the term that is the answer to part (a) better than “nonparametric test...
31 May 2021Efficiency What does it mean when we say that the rank correlation test has an efficiency rating of 0.91 when compared to the parametric test for linear correlation?
31 May 2021Speed Dating Some of the nonparametric methods in this chapter use ranks of data. Find the ranks corresponding to these attractiveness ratings (1 = not attractive; 10 = extremely attractive) of males by females who participated in a speed dating event (from Data Set 18 “Speed Da...
31 May 2021Stock Market: Testing for Randomness Above and Below the Median Listed below are the annual high values of the Dow Jones Industrial Average for a recent sequence of years. Find the median, then test for randomness below and above the median. What does the result suggest about the...
31 May 2021Baseball World Series Victories Test the claim that the sequence of World Series wins by American League and National League teams is random. Given on the next page are recent results, with A = American League and N = National League.
31 May 2021Testing for Randomness of Super Bowl Victories Listed below are the conference designations of teams that won the Super Bowl, where N denotes a team from the NFC and A denotes a team from the AFC. Do the results suggest that either conference is superior?
31 May 2021Newspapers Media experts claim that daily print newspapers are declining because of Internet access. Listed below are the numbers of daily print newspapers in the United States for a recent sequence of years. First find the median, then test for randomness of the numbers above an...
31 May 2021Draft Lottery In 1970, a lottery was used to determine who would be drafted into the U.S. Army. The 366 dates in the year were placed in individual capsules, they were mixed, and then capsules were selected to identify birth dates of men to be drafted first. The first 30 results ...
31 May 2021Odd and Even Digits in Pi A New York Times article about the calculation of decimal places of p noted that “mathematicians are pretty sure that the digits of p are indistinguishable from any random sequence.” Given below are the first 25 decimal places of p. Test for randomness i...
31 May 2021Law Enforcement Fatalities Listed below are numbers of law enforcement fatalities for 20 recent and consecutive years. First find the mean, identify each value as being above the mean (A) or below the mean (B), then test for randomness above and below the mean. Is there a trend?u...
31 May 2021use the following sequence of political party affiliations of recent presidents of the United States, where R represents Republican and D represents Democrat. R R R R D R D R R R D R R R D D R D D R R D R R D R DGood Sample? Given the sequence of data, if we fail to reject rando...
31 May 2021use the following sequence of political party affiliations of recent presidents of the United States, where R represents Republican and D represents Democrat. R R R R D R D R R R D R R R D D R D D R R D R R D R DNotation Identify the values of n1, n2, and G that would be used in...
31 May 2021use the following sequence of political party affiliations of recent presidents of the United States, where R represents Republican and D represents Democrat. R R R R D R D R R R D R R R D D R D D R R D R R D R DTesting for Bias Can the runs test be used to show the proportion o...
31 May 2021Blood Pressure Refer to the measured systolic and diastolic blood pressure measurements of 153 randomly selected males in Data Set 1 “Body Data” in Appendix B and use a 0.05 significance level to test the claim that among men, there is a correlation between systolic blood pressur...
31 May 2021Crickets and Temperature The association between the temperature and the number of times a cricket chirps in 1 min was studied. Listed below are the numbers of chirps in 1 min and the corresponding temperatures in degrees Fahrenheit (based on data from The Song of Insects by Geor...
31 May 2021Measuring Seals from Photos Listed below are the overhead widths (in cm) of seals measured from photographs and the weights of the seals (in kg). The data are based on “Mass Estimation of Weddell Seals Using Techniques of Photogrammetry,” by R. Garrott of Montana State University...
31 May 2021CPI and the Subway Use CPI/subway data from the given data to test for a correlation between the CPI (Consumer Price Index) and the subway
31 May 2021Pizza and the Subway The “pizza connection” is the principle that the price of a slice of pizza in New York City is always about the same as the subway fare. Use the data listed below to determine whether there is a correlation between the cost of a slice of pizza and the subway ...
31 May 2021Ages of Best Actresses and Best Actors Listed below are ages of Best Actresses and Best Actors at the times they won Oscars (from Data Set 14 “Oscar Winner Age” in Appendix B). Do these data suggest that there is a correlation between ages of Best Actresses and Best Actors?
31 May 2021Chocolate and Nobel Prizes The table below lists chocolate consumption (kg per capita) and the numbers of Nobel Laureates (per 10 million people) for several different countries (from Data Set 16 in Appendix B). Is there a correlation between chocolate consumption and the rate of...
31 May 2021use the scatterplot to find the value of the rank correlation coefficient rs and the critical values corresponding to a 0.05 significance level used to test the null hypothesis of Rs = 0. Determine whether there is a correlation.
31 May 2021Level of Measurement Which of the levels of measurement (nominal, ordinal, interval, ratio) describe data that cannot be used with the methods of rank correlation? Explain.
31 May 2021Regression If the methods of this section are used with paired sample data, and the conclusion is that there is sufficient evidence to support the claim of a correlation between the two variables, can we use the methods of Section 10-2 to find the regression equation that can be ...
31 May 2021Requirements Assume that we want to use the data fgiven below. with the KruskalWallis test. Are the requirements satisfied? Explain.
31 May 2021Speed Dating Listed on the top of the next page are attribute ratings of males by females who participated in speed dating events (from Data Set 18 “Speed Dating” in Appendix B ). In using the Kruskal-Wallis test, we must rank all of the data combined, and then we must find the s...
31 May 2021Finding Critical Values Assume that we have two treatments (A and B) that produce quantitative results, and we have only two observations for treatment A and two observations for treatment B. We cannot use the Wilcoxon signed ranks test given in this section because both sample s...
31 May 2021IQ and Lead Exposure Data Set 7 “IQ and Lead” in Appendix B lists performance IQ scores for a random sample of subjects with low lead levels in their blood and another random sample of subjects with high lead levels in their blood. Use a 0.05 significance level to test the claim ...
31 May 2021IQ and Lead Exposure Data Set 7 “IQ and Lead” in Appendix B lists full IQ scores for a random sample of subjects with “medium” lead levels in their blood and another random sample of subjects with “high” lead levels in their blood. Use a 0.05 significance level to test the claim...
31 May 2021Do Men Talk the Same Amount as Women Refer to Data Set 24 “Word Counts” in Appendix B and use the measured word counts from men in the third column and the measured word counts from women in the fourth column. Use a 0.01 significance level to test the claim that contrary to a pop...
31 May 2021Blanking Out on Tests In a study of students blanking out on tests, the arrangement of test items was studied for its effect on anxiety. The following scores are measures of “debilitating test anxiety” (based on data from “Item Arrangement, Cognitive Entry Characteristics, Sex an...
31 May 2021Clinical Trials of Lipitor The sample data below are changes in LDL cholesterol levels in clinical trials of Lipitor (atorvastatin). It was claimed that Lipitor had an effect on LDL cholesterol. (The data are based on results given in a Parke-Davis memo from David G. Orloff, M.D....
31 May 2021Radiation in Baby Teeth Listed below are amounts of strontium-90 (in millibecquerels, or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from Pennsylvania residents and New York residents born after 1979 (based on data from “An Unexpected Rise in Stron...
31 May 2021Sign Test vs. Wilcoxon Signed-Ranks Test Using the data below, we can test for no difference between body temperatures at 8 AM and 12 AM by using the sign test or the Wilcoxon signed-ranks test. In what sense does the Wilcoxon signed-ranks test incorporate and use more informatio...
31 May 2021Body Temperatures For the matched pairs listed below, identify the following components used in the Wilcoxon signed-ranks test: a. Differences d b. The ranks corresponding to the nonzero values of d c. The signed ranks d. The sum of the positive ranks and the sum of the abso...
31 May 2021Wilcoxon Signed-Ranks Test for Body Temperatures The table below lists body temperatures of seven subjects at 8 AM and at 12 AM (from Data Set 3 “Body Temperatures in Appendix B). The data are matched pairs because each pair of temperatures is measured from the same person. Assum...
31 May 2021Procedures for Handling Ties In the sign test procedure described in this section, we exclude ties (represented by 0 instead of a sign of or -). A second approach is to treat half of the 0s as positive signs and half as negative signs. (If the number of 0s is odd, exclude one s...
31 May 2021Old Faithful Refer to Data Set 23 “Old Faithful” in Appendix B for the time intervals before eruptions of the Old Faithful geyser. Use a 0.05 significance level to test the claim that those times are from a population with a median of 90 minutes.
31 May 2021Testing for Median Weight of Quarters Refer to Data Set 29 “Coin Weights” in Appendix B for the weights (g) of randomly selected quarters that were minted after 1964. The quarters are supposed to have a median weight of 5.670 g. Use a 0.01 significance level to test the claim tha...
31 May 2021Testing for Median Weight of Quarters Refer to Data Set 29 “Coin Weights” in Appendix B for the weights (g) of randomly selected quarters that were minted after 1964. The quarters are supposed to have a median weight of 5.670 g. Use a 0.01 significance level to test the claim tha...
31 May 2021Earthquake Depths Refer to Data Set 21 “Earthquakes” in Appendix B for the earthquake depths (km). Use a 0.01 significance level to test the claim that the median is equal to 5.0 km.
31 May 2021Earthquake Magnitudes Refer to Data Set 21 “Earthquakes” in Appendix B for the earthquake magnitudes. Use a 0.01 significance level to test the claim that the median is equal to 2.00.
31 May 2021