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- To test the fairness of law enforcement in Bartow County, a local citizens' group want to know whether women and men are unequally likely to get speeding tickets. Two hundred adults in Bartow County are randomly phoned and asked whether or not they had been cited for speeding in the last year. For a sample of 114 women, 12 were ticketed and 102 were not ticketed. For a sample of 86 men, 11 were ticketed and 75 were not ticketed. Use a 0.05 level of significance to test the claim that women and men are unequally likely to get speeding tickets. Women are sample proportion 1. Men are sample proportion 2. What is the z-test statistic for this problem? Round the answer to two decimal places. What is the p-value for this problem? Round the answer to three decimal places. What is the conclusion when you compare the p-value and the level of significance,? What is the conclusion based on the original claim?A group of 1440 students was surveyed in October 2018 about their sleeping patterns and consumption of caffeinated beverages. Of the 1440 students asked, 834 said they had trouble falling asleep at night, but the rest did not. Of the 834 who said they had trouble sleeping at night, 640 drank some type of caffeinated beverage after 2 pm most days. Of those who reported no trouble falling asleep at night, 108 said they drank some type of caffeinated beverage after 2 pm most days.A study in Boston schools questioned third graders to see if they felt stress in their school life. Out of 37 boys, 18 said they felt stress. While 16 out of 54 girls said they felt stress. Is this enough evidence to show that the boys and girls experience stress differently?
- Suppose we want to compare the GPA for students in at least three different social classes (Upper, Middle, Working). We obtain GPA records for a randomly selected set of 30 students, ten from each social class group. What test should you use and why?A local government official observes an increase in the number of individuals with cardiovascular and obesity problems in his barangay. In order to improve the health conditions of his constituents, he aims to promote an easy and cheap way to reduce weight. It is known that obesity results in risk of having illnesses like diabetes and heart problems. He encouraged his constituents to participate in his "Dance for Life" project every weekend for three months. To know if the program is effective in reducing weight, he randomly selected 12 participants from the group who completed the program. The weight loss data, in kilograms, of the 12 randomly selected participants after completing the program, are 0.5, 0.7, 0.9, 1.1, 1.2, 1.3, 1.4, 2.0, 2.3, 2.4, 2.7, 3.0. It is known that the weight loss of those who have completed the dance program follows a normal distribution with variance of 3.24 ??2. a. Construct and interpret a 90% confidence interval for the true mean weight loss of the…According the the U.S. Census bureau, the percentage of Santa Ana residents with a bachelor's degree or higher is 14% and the percentage of Irvine residents with a bachelor's degree or higher is 68.5%. Suppose that the sample sizes were 1000 for the Santa Ana group and 1000 for the irvine group. Is there enough evidence to conclude that people who live in Irvine have a higher level of education compared to people living in Santa Ana?
- Researchers studied the behavior of birds that were searching for seeds and insects in an Oregon forest. In this forest, 54% of the trees were Douglas firs, 40% were ponderosa pines, and 6% were other types of trees. At a randomly selected time during the day, the researchers observed 156 red-breasted nuthatches: 70 were in Douglas firs, 79 in ponderosa pines, and 7 in other types of trees. Do these data provide convincing evidence that nuthatches prefer particular types of trees when they’re searching for seeds and insects?In a study about learning styles, researchers used a group of 64 elementary school students who volunteered to be part of the study. The researchers gave each student a pre-test and based upon the results, they divided them into 32 pairs of similarly scoring students. School administrators then randomly assigned one student from each pair to mathematics instruction online while the other student received in-person instruction in a traditional classroom. At the end of the year, all 64 students received a mathematics assessment, measured on a 100-point scale. The researchers calculated the difference (in person −− online) in the mathematics assessment scores for each pair of students. The 32 differences had a mean of 15 and a standard deviation of 3.9 points. Construct and interpret a 95% confidence interval for the mean difference (in person −− online) in the mathematics assessment scores for all pairs of students like these who learn math either face-to-face or online.As a destination marketing director, you found that TV executives used the guideline that 25% of the viewers were watching Fox cable network, 22% watching NBC and CBS, and 19% watching ABC. The remaining 12% were watching other cable networks such as CNN and MSNBC on a weekday night. A random sample of 500 viewers in the D.C. metro area last Tuesday night showed 109 homes were tuned in to the Fox station, 125 homes tuning in to NBC affiliate, 100 homes tuning in to CBS affiliate and 81 homes tuning in to ABC affiliate. 85 homes were watching CNN and NSNBC cable stations. At the 0.05 significant level, can we conclude that the guideline is still reasonable?
- The school district sets up two locations to help students with technical difficulties over the summer. They believe the technicians they have assigned to location 2 are being lazy and not helping students as much as they should be so they take a random sample of 15 students from each of the two locations and ask if their technical issue had been resolved (over 200 students had asked for assistance at each location). Twelve of the 15 students from location 1 reported their technical issue had been resolved and 8 of the 15 students from location 2 reported their technical issue had been resolved. Is this convincing evidence that the technicians from location 2 are being lazy and not helping students as much as those from location 1?Sierra College students enrolled in an online Elementary Statistics course were asked to participate in an anonymous onlne survey. The survey asked the students "Which type of device will you primarily use to access your online course in Canvas?". Of the 152 students who answered this question, 20 responded "a desktop computer", 121 responded "a laptop computer", 6 responded "a smartphone", and 5 responded "a tablet". The Sierra College Mathematics Department believes that less than 5% of students enrolled in an online Elementary Statistics course primarily uses a smartphone to access their online course in Canvas. Use the data collected in the survey to conduct a hypothesis testing procedure to test this belief. What conclusion should be reached according to the results of this hypothesis test?During the pandemic, an HR manager randomly assigned 6 employees to work from homeand the other 6 employees to work from the office as usual. After three months, all 12employees’ job performance was tested. Scores for those working from home were 10, 12,14, 13, 11, 12, and scores for those who worked from the office were 8, 6, 10, 8, 9, and 7.The HR manager then compares the scores from both groups to determine which groupscores significantly higher.Based on the experiment above,a) Carry out a t-test using five steps of hypothesis testing with the 0.05 level ofsignificance at one-tailed. Explain your finding.b) Sketch the t-distribution involved.