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- A company conducted a survey of its employees to collect information about the travel time of the employees from their homes towards its offices. In response to the question on commute, 60% said they travelled one hour per day, 25% reported they travelled two hours per day, and 15% reported they travelled three hours per day. The next year, upon observing changes in the condition of the roads and the number of commuters travelling on a regular basis, the company again conducted a survey to check for the travel time of the employees. The following data were gathered: Based on the data, is there evidence of a shift in the distribution of responses to the travel time question a year after initial question was made? Run the test at a 5% level of significance.Random samples of 900 people in the United States and in Great Britain indicated that 60% of the people in the United States were positive about the future economy, whereas 66% of the people in Great Britain were positive about the future economy. Does this provide strong evidence that the people in Great Britain are more optimistic about the economy (alpha = 0,01)?In a clinical trial, 24 out of 880 patients taking a prescription drug daily complained of flulike symptoms.Suppose that it is known that 2.3% of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than 2.3% of this drug's users experience flulike symptoms as a side effect at the α=0.01 level of significance?
- A sample of men and women who had passed their driver's test either the first time or the second time were surveyed, with the following results: Results of the driving testGender First time Second timeMen 126 211Women 135 178a) Do these data suggest that there is a relationship between gender and the passing of their driver’s test from which the present sample was drawn? Let alpha=.05A sociologist wants to investigate the question, "Is there a relationship between texting during class and grade-point-average (GPA) among high school seniors in a large district?" Which study design is most appropriate? Before the semester starts, randomly select 40 seniors from each high school who do not text during class. Assign 20 to the texting treatment group (text three or more times during every class meeting) and 20 to the control group (no texting during class). At the end of the semester, obtain each student’s GPA from the appropriate admissions and records office. Compare the GPA of students who routinely text during class to the GPA of students who do not text during class. Before the semester starts, randomly select 40 seniors from each high school who do not text during class. Assign 20 to the texting treatment group (text three or more times during every class meeting) and 20 to the control group (no texting during class). At the end of the semester,…Do well-rounded people get fewer colds? A study on the Chronicle of Higher Education was conducted by scientist at Carnegie Mellon University, the University of Pittsburgh and the University of Virginia. They found that people who have only a few social outlets get more colds than those who are involved in a variety of social activities. Suppose that of the 276 healthy men and women tested, n1=96 had only a few social outlets and n2=105 were busy with six or more activities. When these people were exposed to a cold virus, the following results were observed: Construct a 99% confidence interval for the difference in the two population proportions.
- A researcher notes that there seems to be a difference in the prevalence of individuals who are medication adherent and have high levels of education along with a high health literacy and the prevalence of individuals who are not medication adherent and have low levels of education along with a low health literacy. Use the appropriate hypothesis to determine if education level and health literacy status are related (independent) at the 5%. Low Level of Education Low Medication Adherence High Medication Adherence Total Low Health Literacy 91 9 100 High Health Literacy 9 291 300 Total 100 300 400 High Level of Education Low Medication Adherence High Medication Adherence Total Low Health Literacy 96 4 100 High Health Literacy 4 296 300 Total 100 300 40031% of all pygmy softshell toises have stripes on their shells. A herpetologist in Cititon collects a sample of 28 pygmy softshell tortoises and finds that 8 of them have stripes on their shells. Is there enough evidence to conclude, at a significance of alpha=0.05, that the proportion of pygmy softshell tortoises in Cititon with stripes on their shells is less than 31%? What is the claim? What is the null hypothesis? What is the alternative hypothesis? What is the test statistic? What is/are the critical value(s)? Do we reject the null hypothesis? What conclusion do we draw? What is the P-value for the problem above?An experiment to determine if a migraine medication decreases a person's average number of monthly migraines is performed on 400 people who report they have several migraines a month. Researchers randomly assigned 200 people to the treatment group and 200 people to the control group. After the study, the researchers determined that 48 of the subjects in the treatment group and 28 of the subjects in the control group average fewer migraines per month. The data from the two groups are resampled 150 times, and the table shows the distribution of the differences of the proportions for the reconfigured treatment and control groups.
- A consumer advocacy group wanted to study whether different airline carriers differed in terms of their delayed flights. In particular, the researchers were interested in the relationship between p1, the proportion of Alpha Airlines flights that were delayed at least 15 minutes, and p2, the proportion of Beta Airlines flights that were delayed at least 15 minutes. A random sample of 1,000 Alpha flights and a separate random sample of 1,000 Beta flights found that 67 of the Alpha fights and 160 of the Beta flights were delayed at least 15 minutes. The conditions for inference were checked and verified. Does this set of samples provide strong evidence that Alpha Airlines has a smaller proportion of flights that are delayed at least 15 minutes than Beta Airlines, at the α = 0.05 significance level? Find the z-table here. A. The test statistic is z = –6.56 and the P-value ≈ 0. Since the P-value ≈ 0 < 0.05, there is not sufficient evidence that Alpha Airlines has fewer delayed…A college president wanted to know how 10-year-after-graduation salaries for aca- demic majors (English, psychology, math, etc.) compared to salaries for career-oriented majors (business, engineering, computer science, etc.). She matched 84 academic majors at her college with 84 career-oriented majors on the basis of SAT scores and GPA. She found MAcademic = $59,250, MCareer =$61,000, sD = 9,500. Use an alpha of .05 and a two-tailed test to determine if there is a difference in salaries.4) A medical researcher is interested in determining if there is a relationship between adults over 50 who exercise regularly and low, moderate, and high blood pressure. A random sample of 236 adults over 50 is selected and the results are given below. Test the claim that regular exercise and low, moderate, and high blood pressure are independent. Use alpha= 0.01 Blood pressure: Reg exercise: low 35, moderate 62, high 25 No reg. Exercise: low 21, moderate 65, high 28