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(a) determine the test statistic, H, (b) determine the critical value at the o = 0.05 level of significance, and (c) test whether the distributions of the populations are different. X Y Z 13 18 12 18 14 17 11 12 | 13 15Crash Data The Insurance Institute for Highway Safety conducts experiments in which cars are crashed into a fixed barrier at 40 mph. In a 40-mph offset test, 40%% of the total width of each vehicle strikes a barrier on the driver side. The barrier's deformable face is made of aluminum honeycomb, which makes the forces in the test similar to those involved in a frontal offset crash between two vehicles of the same weight, each going just less than 40 mph. You are in the market to buy a new family car, and you want to know whether the distribution of head injury resulting from this offset crash is the same for large family cars, passenger vans, and midsize utility vehicles at the a = 0.01 level of significance. The following data were collected from the study. Source: Insurance Institute for Highway Safety Large Family Head Injury Passenger Head Injury Midsize Utility Head Injury Cars [hic)) Vans (hic) Vehicles (hic) Hyundai Toyota 284 148 Honda Pilot 225 XG300 Sienna Honda Ford Taurus 134 238 Toyota 4Runner 216 Odyssey Buick Mitsubishi 409 Ford Freestar 340 186 LeSabre Endeavor Chevrolet 530 Mazda MPV 803 Nissan Murano 307 Impala Chevrolet Chrysler 300 149 550 Ford Explorer 353 Uplander Pontiac 627 Nissan Quest 470 Kia Sorento 411 Grand Prix Toyota Avalon 186 Kia Sedona 322 Chevy Trailblazer 397(a) determine the test statistic, H, (b) determine the critical value at the o = 0.05 level of significance, and (c) test whether the distributions of the populations are different. X Y Z 7 4 4 3 10 7Births by Day of Week An obstetrician knew that there were more live births during the week than on weekends. She wanted to discover whether the distribution for number of births was the same for each of the 5 days of the week. She randomly selected eight dates for each of the 5 days of the week and obtained the data shown. Source: National Center for Health Statistics. MONDAY TUESDAY |WEDNESDAY THURSDAY FRIDAY 10.456 11,821 11,084 11,171 11.545 10.023 11.944 11.570 11,745 12,321 10.691 11.045 11.348 12.023 11.749 10.283 12,927 11,875 12.433 12,192 10.285 12,577 12,193 12.132 12,422 11,189 11,753 11.593 11,903 11,827 11,198 12,509 11,216 11,233 11,824 11,465 13,521 11,818 12.543 12,543 (a) State the null and alternative hypotheses. (b) The sums of the ranks in each category are as follows: MONDAY TUESDAY WEDNESDAY THURSDAY| FRIDAY Sample size 8 8 8 Sum of ranks 48 226 144 194.5 207.5 Use this information to compute the test statistic. (c) What is the critical value at the a = 0.05 level of significance? (d) State your conclusion. (e) Draw side-by-side boxplots to support your conclusion.Births by Season An obstetrician wants to determine if the distribution of births is the same for the periods January to March April to June, July to September, and October to December. She randomly selected 10 days within each time frame and obtained the results shown in the following table: Source: National Center for Health Statistics. January-March April-June July-September| October-December 10.456 10,799 11,485 11,281 11,574 11,743 12,475 11,406 12 321 11,857 12,454 11,827 11,651 11,808 12,193 8.708 8,521 10,982 11.244 12,022 11,621 9.184 12,081 11,930 11,321 12,357 11,387 11.054 7,706 12,251 9.055 11,431 10.872 11,918 12,319 12,818 10.837 11,212 12.927 10,824 (a) State the null and alternative hypotheses. (b)The sums of the ranks in each category are as follows: January-March April-June | July-September | October-December Sample size 10 10 10 10 Sum of ranks 149 207 287 197 Use this information to compute the test statistic. (c) What is the critical value at the a = 0.05 level of significance? (d) State your conclusion. (e) Draw side-by-side boxplots to support your conclusion.Corn Production The following data represent the number of corn plants in randomly sampled rows (a 17-foot by 5-inch strip) for various types of plot. Source: Andrew Dieter and Brad Schmidgall, Joliet Junior College Plot Type Number of Plants Sludge plot 25 27 33 30 28 27 Spring disk 32 30 33 35 34 34 No til Spring Chisel 30 2 Do the data indicate that the distribution for each type of plot is the same at the o = 0.05 level of significance?Soybean Yield The following data represent the number of pods on a random sample of soybean plants for various types of plot Source: Andrew Dieter and Brad Schmidgall, Joliet Junior College Plot Type Pods Liberty Fall plowed No till Chisel plowed Round-up ready Do the data indicate that the distribution for each type of plot is the same at the o = 0.05 level of significance?Reaction Time In an online psychology experiment sponsored by the University of Mississippi, researchers asked study participants to respond to various stimuli. Participants were randomly assigned to one of three groups. Subjects in the simple group were required to respond as quickly as possible after a stimulus was presented. Subjects in the goo-go group were required to respond to a particular stimulus while disregarding other stimuli. Finally, subjects in the choice group needed to respond differently to different stimuli. Depending on the type of whistle sound, the subject had to press a certain button. The reaction time (in seconds) for each stimulus is presented in the following table: Source: Psych Experiments; University of Mississippi, www.olemiss.edu/psychexps/. Simple | Go/No-Go | Choice 0.430 0.588 0.581 0.498 0.375 0.498 0.480 0.409 0.519 0.376 0.613 0.538 0.402 0.481 0.484 0.320 0.355 0.725 Is the distribution for each stimulus the same at the a = 0.01 level of significance?Math Scores Researchers wanted to compare math test scores of students at the end of secondary school from various countries. Eight randomly selected students from Canada, Denmark, and the United States each were administered the same exam; Source: Based on data obtained from the International Association for the Evaluation of Educational Achievement Canada Denmark United States 578 548 568 563 506 458 548 530 530 535 518 456 521 502 571 581 485 513 555 492 589 513 480 491 Can the researchers conclude that the distribution of exam scores is the same for each country at the a = 0.01 level of significance?Crash Data The Insurance Institute for Highway Safety conducts experiments in which cars are crashed into a fixed barrier at 40 mph. In a 40-mph offset test, 40%% of the total width of each vehicle strikes a barrier on the driver side. The barrier's deformable face is made of aluminum honeycomb, which makes the forces in the test similar to those involved in a frontal offset crash between two vehicles of the same weight, each going just less than 40 mph. You are in the market to buy a new family car, and you want to know whether the distribution of chest compression resulting from this crash is the same for each vehicle category at the a = 0.01 level of significance. The following data were collected from the study. Source: Insurance Institute for Highway Safety Large Chest Chest Midsize Chest Passenger Family Compression Compression Utility Compression Vans Cars (mm) (mm) Vehicles (mm] Hyundai Toyota 33 Honda Pilot 29 XG300 Sienna Ford Honda Toyota 40 28 38 Taurus Odyssey 4Runner Buick Ford Mitsubishi 28 27 35 LeSabre Freestar Endeavor Chevrolet Mazda Nissan 30 30 32 Impala MPV Murano Chrysler Chevrolet 34 26 Ford Explorer 34 300 Uplander Pontiac Nissan 34 33 Jeep Liberty 42 Grand Prix Quest Toyota Kia Buick 31 36 29 Avalon Sedona Rendezvous