In a study of the effectiveness oFa fabric device that acts like a support stocking for a weak or damaged heart, 110 people who consented to treatment were assigned at random to either a standard treatment consisting of drugs or the experimental treatment that consisted of drugs plus surgery to install the stocking. After two years, 40% of the 50 patients receiving the stocking had improved and 26% of the patients receiving the standard treatment had improved. [Use a statistical computer package to calculate the Pvalue. Use Pexperimental Pstandard- Round your test statistic to two decimal places and your P-value to four decimal places.) Do these data provide convincing evidence that the proportion of patients who improve is higher for the experimental treatment than for the standard treatment? Test the relevant hypotheses using a signicance level of 0.05. 0 Yes ONO The authors of the paper "Age and Violent Content Labels Make Video Games Forbidden Fruits for Youth" carried out an experiment to determine if restrictive labels on video games actually increased the attractiveness of the game for young game players.1' Participants read a description ofa new video game and were asked how much they wanted to playr the game. The description also included an age rating. Some participants read the descripon with an age restrictive label of ?+, indicating that the game was not appropriate for children under the age of ?. Others read the same description, but with an age restrictive label of 12+, 16+, or 18+. The data below for 12 to 13yearold boys are ctitious, but are consistent with summary statistics given in the paper. (The sample sizes in the actual experiment were larger.) For purposes of this exercise, you can assume that the boys were assigned at random to one of the four age label treatments (?+, 12+, 16+, and 18+). Data shown are the boys' ratings of how much they wanted to play the game on a scale of 1 to 10. ?+ label 12+ label 16+ label 18+ label 7 8 T" 10 7 9 9 5 8 6 5 6 10 5 T" T" 8 5 6 6 8 8 l 9 9 2 6 10 4 I" 8 Do the data provide convincing evidence that the mean rating associated with the game description by 12- to 13year-old boys is not the same for all four restrictive rating labels? Test the appropriate hypotheses using a significance level of 0.05. Calculate the test statistic. [Round your answer to two decimal places.) F=x To determine if chocolate milk was as effective as other carbohydrate replacement drinks, nine male cyclists performed an intense workout followed by a drink and a rest period. At the end of the rest period, each cyclist performed an endurance trial where he exercised until exhausted and time to exhaustion was measured. Each cyclist completed the entire regimen on two different days. On one day the drink provided was chocolate milk and on the other day the drink provided was a carbohydrate replacement drink. Data consistent with summary quantities appear in the table below. (Use a statistical computer package to calculate the P-value. Subtract the carbohydrate replacement times from the chocolate milk times. Round your test statistic to two decimal places, your of down to the nearest whole number, and the P-value to three decimal places.) Cyclist Time to Exhaustion (minutes) 1 2 3 4 5 6 7 8 g Chocolate Milk 55.47 22.12 21.03 44.59 52.21 28.93 51.76 30.25 27.19 Carbohydrate Replacement 20.28 25.77 34.88 16.10 38.10 39.91 30.35 9.79 10.42 t= df = P = Is there sufficient evidence to suggest that the mean time to exhaustion is greater after chocolate milk than after carbohydrate replacement drink? Use a significance level of 0.05. O Yes O NoTo investigate the fluid mechanics of swimming, twenty swimmers each swam a specified distance in a water-filled pool and in a pool where the water was thickened with food grade guar gum to create a syrup-like consistency. Velocity, in meters per second, was recorded and the results are given in a table below. The researchers concluded that swimming in guar syrup does not change swimming speed. (Use a statistical computer package to calculate the P-value. Use ud = /water - /guar syrup. Round your test statistic to two decimal places and the P-value to three decimal places.) Swimmer Velocity (m/s) Water Guar Syrup 1.87 1.10 1.52 1.35 3 ..59 1.70 4 1.51 1.41 5 1.60 1.09 6 1.36 0.91 7 1.09 1.55 8 1.74 1.53 9 1.46 1.72 10 1.62 1.97 11 0.94 .78 12 ..53 .22 13 1.89 1.82 14 1.22 1.4 15 1.91 L.33 16 1.37 1.78 17 1.82 1.27 18 1.91 1.07 19 ..03 1.00 20 1.00 1.31 t= df = P = Is there sufficient evidence to suggest that there is any difference in swimming time between swimming in guar syrup and swimming in water? Carry out a hypothesis test using a = 0.01 significance level. Yes O NoSome commercial airplanes recirculate approximately 50% of the cabin air in order to increase fuel efficiency. The researchers studied 1096 airline passengers, among which some traveled on airplanes that recirculated air and others traveled on planes that did not recirculate air. Of the 515 passengers who flew on planes that did not recirculate air, 104 reported post-flight respiratory symptoms, while 112 of the 581 passengers on planes that did recirculate air reported such symptoms. Is there sufficient evidence to conclude that the proportion of passengers with post-flight respiratory symptoms differs for planes that do and do not recirculate air? Test the appropriate hypotheses using