Solved: In 310, use the Wilcoxon matched-pairs signedranks test to test the given

A researcher believes the median from population 1 is less than the median from population 2 in matched-pairs data. How would you define MD? How would you compute the differences?

When conducting a left-tailed Wilcoxon matched-pairs signedranks test, the test statistic is T = .

In Problems 310, use the Wilcoxon matched-pairs signedranks test to test the given hypotheses at the a = 0.05 level of significance. The dependent samples were obtained randomlyHypotheses: H0: MD = 0 versus H1: MD 7 0 with n = 12 and T- = -16

In Problems 310, use the Wilcoxon matched-pairs signedranks test to test the given hypotheses at the a = 0.05 level of significance. The dependent samples were obtained randomlyHypotheses: H0: MD = 0 versus H1: MD 7 0 with n = 20 and T- = -65.

In Problems 310, use the Wilcoxon matched-pairs signedranks test to test the given hypotheses at the a = 0.05 level of significance. The dependent samples were obtained randomly Hypotheses: H0: MD = 0 versus H1: MD 6 0 with n = 15 and T+ = 33.

In Problems 310, use the Wilcoxon matched-pairs signedranks test to test the given hypotheses at the a = 0.05 level of significance. The dependent samples were obtained randomly Hypotheses: H0: MD = 0 versus H1: MD 6 0 with n = 25 and T+ = 95.

In Problems 310, use the Wilcoxon matched-pairs signedranks test to test the given hypotheses at the a = 0.05 level of significance. The dependent samples were obtained randomlyHypotheses: H0: MD = 0 versus H1: MD 0 with n = 18, T- = -121, and T+ = 50.

In Problems 310, use the Wilcoxon matched-pairs signedranks test to test the given hypotheses at the a = 0.05 level of significance. The dependent samples were obtained randomlyHypotheses: H0: MD = 0 versus H1: MD 0 with n = 14, T- = -45, and T+ = 60.

In Problems 310, use the Wilcoxon matched-pairs signedranks test to test the given hypotheses at the a = 0.05 level of significance. The dependent samples were obtained randomlyHypotheses: H0: MD = 0 versus H1: MD 7 0 with n = 40 and T- = -300.

In Problems 310, use the Wilcoxon matched-pairs signedranks test to test the given hypotheses at the a = 0.05 level of significance. The dependent samples were obtained randomly Hypotheses: H0: MD = 0 versus H1: MD 6 0 with n = 35 and T+ = 210.

Effects of Exercise To determine the effectiveness of an exercise regimen, a physical therapist randomly selects 10 women to participate in a study. She measures their waistlines (in inches) both before and after a rigorous 8-week exercise program and obtains the data shown. Is the median waistline before the exercise program more than the median waistline after the exercise program? Use the a = 0.05 level of significance. Woman Before After Woman Before After 1 23.5 19.75 6 19.75 19.5 2 18.5 19.25 7 35 34.25 3 21.5 21.75 8 36.5 35 4 24 22.5 9 52 51.5 5 25 25 10 30 31

Effects of Exercise A physical therapist wishes to learn whether or not an exercise program increases flexibility. She measures the flexibility (in inches) of 12 randomly selected subjects both before and after an intensive 8-week training program and obtains the data shown. Is the median flexibility before the exercise program less than the median flexibility after the exercise program? Use the a = 0.05 level of significance. Subject Before After Subject Before After 1 18.5 19.25 7 19.75 19.5 2 21.5 21.75 8 15.75 17 3 16.5 16.5 9 18 19.25 4 21 20.25 10 22 19.5 5 20 22.25 11 15 16.5 6 15 16 12 20.5 20

Reaction Time In an experiment conducted online at the University of Mississippi, participants are asked to react to a stimulus. In one particular experiment, the participant must press a key upon seeing a blue screen. The time to press the key (in seconds) is measured. The same person is then asked to press a key upon seeing a red screen, again with the time to react measured. The results for six study participants are shown. Does the evidence suggest that the median reaction time to the blue stimulus is different from the median reaction time to the red stimulus? Use the a = 0.05 level of significance. Participant Number Reaction Time to Blue Reaction Time to Red 1 0.582 0.408 2 0.481 0.407 3 0.841 0.542 4 0.267 0.402 5 0.685 0.456 6 0.450 0.533 Source: PsychExperiments at the University of Mississippi

Reaction Time In an experiment conducted online at the University of Mississippi, participants are asked to react to a stimulus. In one particular experiment, the participant must press a key upon seeing a blue screen. The time to press the key (in seconds) is measured. The same person is then asked to press a key upon seeing a red screen, again with the time to react measured. The results for six study participants are shown. Does the evidence suggest that the median reaction time to the blue stimulus is different from the median reaction time to the red stimulus? Use the a = 0.05 level of significance. Participant Number Reaction Time to Blue Reaction Time to Red 1 0.582 0.408 2 0.481 0.407 3 0.841 0.542 4 0.267 0.402 5 0.685 0.456 6 0.450 0.533 Source: PsychExperiments at the University of Mississippi Rat H-L3 H-R0 Rat H-L3 H-R0 1 15.2 15.8 7 14.3 16.4 2 16.1 16.5 8 14.5 16.5 3 15.3 16.7 9 15.2 16.0 4 16.4 15.7 10 16.1 16.8 5 15.7 16.9 11 15.1 17.6 6 14.7 13.1 12 15.8 16.9 Source: NASA Life Sciences Data Archive

Secchi Disk A Secchi disk is an 8-inch-diameter weighted disk painted black and white and attached to a rope. The disk is lowered into water, and the depth (in inches) at which it is no longer visible is recorded. The measurement is an indication of water clarity. An environmental biologist is interested in discovering whether the water clarity of the lake at Joliet Junior College is improving. She takes measurements at the same location during the course of a year and repeats the measurements on the same dates 5 years later. She obtains the results shown. Do you believe that the clarity of the lake is improving? Use the a = 0.05 level of significance. Observation Date Initial Depth Depth 5 Years Later 1 5/11 38 52 2 6/7 58 60 3 6/24 65 72 4 7/8 74 72 5 7/27 56 54 6 8/31 36 48 7 9/30 56 58 8 10/12 52 60 Source: Virginia Piekarski, Joliet Junior College

Effect of Aspirin on Blood Clotting Blood clotting is due to a sequence of chemical reactions. The protein thrombin initiates blood clotting by working with another protein, prothrombin. It is common to measure an individuals blood clotting time as prothrombin time, the time between the start of the thrombin prothrombin reaction and the formation of the clot. Researchers wanted to study the effect of aspirin on prothrombin time. They randomly selected 12 subjects and measured the prothrombin time (in seconds) without taking aspirin and 3 hours after taking two aspirin tablets. They obtained the following data. Does the evidence suggest that aspirin affects the median time it takes for a clot to form? Use the a = 0.05 level of significance. Subject Before Aspirin After Aspirin Subject Before Aspirin After Aspirin 1 12.3 12.0 7 11.3 10.3 2 12.0 12.3 8 11.8 11.3 3 12.0 12.5 9 11.5 11.5 4 13.0 12.0 10 11.0 11.5 5 13.0 13.0 11 11.0 11.0 6 12.5 12.5 12 11.3 11.5 Source: Donald Yochem and Darrell Roach. Aspirin: Effect of Thrombus Formation Time and Prothrombin Time of Human Subjects. Angiology, 22:7076, 1971

Car Rentals The following data represent the weekday rental rate for a compact car charged by two car-rental companies, Avis and Hertz, in 11 locations. Is Avis cheaper than Hertz? Use the a = 0.05 level of significance.

Does Octane Affect Miles per Gallon? A researcher wants to know if the octane level of gasoline affects the gas mileage of a car. She randomly selects 10 cars and puts 5 gallons of 87-octane gasoline in the tank. On a closed track, each car is driven at 50 miles per hour until it runs out of gas. The experiment is repeated, with each car getting 5 gallons of 92-octane gasoline. The miles per gallon for each car are then computed. The results are shown. Would you recommend purchasing 92 octane? Why or why not? 87 Octane 92 Octane 87 Octane 92 Octane 18.0 18.5 23.4 22.8 23.2 23.1 23.1 23.5 31.5 31.9 19.0 19.5 24.9 26.7 26.8 26.2 24.1 25.1 31.8 30.7

Rats Red Blood Cell Counts Researchers at NASA wanted to learn the effects of spaceflight on a rats red blood cell count (RBC). The following data represent the RBC at lift-off minus 3 days (RBC-L3) and immediately upon return (RBC-R0) of 27 rats sent to space on the Spacelab Sciences 1 flight. Rat RBC-L3 RBC-R0 Rat RBC-L3 RBC-R0 112 7.53 8.16 79 7.79 8.52 145 7.79 9.15 47 8.24 8.59 15 7.84 9.09 109 7.69 7.29 142 6.86 8.42 13 7.23 8.93 45 7.93 8.96 74 7.83 8.64 150 7.48 9.25 126 8.09 9.65 162 7.94 7.40 157 8.27 8.76 136 7.95 9.55 156 7.27 9.11 127 8.44 9.38 128 8.23 9.81 153 6.70 9.66 99 14.50 9.86 97 6.95 8.83 90 7.73 9.90 94 6.73 8.46 82 7.31 7.64 124 7.21 9.04 55 7.84 9.54 117 6.95 9.48 Source: NASA Life Sciences Data Archive. They used MINITAB to test whether the RBC three days prior to lift-off was different from the RBC upon return. The results are as follows:

Reaction-Time Experiment Researchers at the University of Mississippi wanted to learn the reaction times of students to different stimuli. In the data that follow, the reaction times for subjects were measured after they received a simple stimulus and a go/no-go stimulus. The simple stimulus was an auditory cue, and the time from when the cue was given to when the student reacted was measured. The go/no-go stimulus required the student to respond to a particular stimulus and not respond to other stimuli. Again, the reaction time was measured. The following data were obtained: Subject Number Simple Go/No-Go Subject Number Simple Go/No-Go 1 0.220 0.375 16 0.498 0.565 2 0.430 1.759 17 0.262 0.402 3 0.338 0.652 18 0.620 0.643 4 0.266 0.467 19 0.300 0.351 5 0.381 0.651 20 0.424 0.380 6 0.738 0.442 21 0.478 0.434 7 0.885 1.246 22 0.305 0.452 8 0.683 0.224 23 0.281 0.745 9 0.250 0.654 24 0.291 0.290 10 0.255 0.442 25 0.453 0.790 11 0.198 0.347 26 0.376 0.792 12 0.352 0.698 27 0.328 0.613 13 0.285 0.803 28 0.952 1.179 14 0.259 0.488 29 0.355 0.636 15 0.200 0.281 30 0.368 0.391 Source: PsychExperiments at The University of Mississippi The researchers used MINITAB to test whether the simple stimulus had a lower reaction time than the go/no-go stimulus. The results of the analysis are as follows:

Outpatient Treatment The median length of stay for substance-abuse outpatient treatment completers is 107 days for those referred by the criminal justice system. The following data represent the length of stays for a random sample of substanceabuse outpatient treatment completers who were referred by an employer. 80 108 95 107 89 100 85 102 115 109 99 94 Source: Department of Health and Human Services Using the Wilcoxon signed-ranks test at the a = 0.05 level of significance, does the median length of stay seem different for employer referrals than for those referred by the criminal justice system?

Outpatient Treatment The median length of stay for male substance-abuse outpatient treatment completers is 105 days. The following data represent the length of stays for a random sample of female substance-abuse outpatient treatment completers. 117 111 81 110 103 94 92 91 116 108 98 84 Source: Department of Health and Human Services Using the Wilcoxon signed-ranks test at the a = 0.05 level of significance, does the median length of stay seem different for males and females?

You Explain It! Dietary Habits A student in an exercise science program wishes to study dietary habits of married couples. She surveys married couples from her local gym and asks them (individually) what percent of their daily calories are from fat. She analyzes the results using the Wilcoxon signed-ranks test. Explain why her results are questionable.