The following table summarizes the results from a two-factor, independent measures study with two levels of factor A and four levels of factor B using a separate sample of n = 5 participants in each treatment condition. Fill in the missing values. Determine if any of the F-statistics are significant at a = .05. Source SS df MS Between Treatments Factor A 20 F= Factor B 12 F= AxB Interaction F= Within Treatments 64 Total
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- What is meant by the sample space of an experiment?The following table summarizes the results from a two-factor study with two levels of factor A and four levels of factor B using a separate sample of n=5 participants in each treatment condition. Fill in the missing values. Determine if any of the F-statistics are significant at . Source SS df MS Between Treatments ____ ____ Factor A 20 ____ ____ F=____ Factor B __ ____ 12 F=____ AxB Interaction ____ ____ 6 F=____ Within Treatments 64 ____ ____ Total ____ ____A 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,…
- 3. Research suggests that depression significantly increases the risk of developing dementia later in life. Suppose that in a study involving 949 elderly persons, it was found that 22% of those who had depression went on to develop dementia, compared to only 17% of those who did not have depression. a) Describe the relevant population and the sample.b) Are the numbers 22% and 17% associated with the population or a sample?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 sample of 15 maple trees in Vermont were treated with one of three amounts of fertilizer, Low (group 1), Medium (group 2) and High (group 3). The volume in sap (measured in mL) produced by each tree was recorded, and a Single-Factor ANOVA test was performed, which ended up rejecting . The Summary table and the ANOVA table produced by Excel are given below: SUMMARY Groups Count Sum Average Variance Low 5 398.1 79.62 27.572 Medium 5 477.2 95.44 3.703 High 5 445.1 89.02 11.357 ANOVA Source of Variation SS df MS F Between Groups 633.0813333 2 316.5406667 22.27486395 Within Groups 170.528 12 14.21066667 Total 803.6093333 14 If you follow up the ANOVA test with a FORMAL Fisher's LSD Pairwise Comparison (PWC) test on , then use the information provided in the Excel-generated output to calculate the value of the Test Statistic (TS) that you would use to perform this PWC test. Round off your final answer to the…
- Suppose a study was conducted to compare the sleep deprivation rates of Californians and Oregonians. The proportion of California residents who reported insufficient rest or sleep during each of the preceding 30 days is 8.8%, while this proportion is 7% for Oregon residents. These data are based on simple random samples of 1,545 California and 1,460 Oregon adult residents. a) Conduct a hypothesis test to determine if these data provide strong evidence the rate of sleep deprivation is different for the two states. Use California as Group A and Oregon as Group B.Test statistic (Round to 4 decimal places): p-value (round to 4 decimal places): Conclusion at the 5% level of significance: We accept the null hypothesis. We reject the null hypothesis. We fail to reject the null hypothesis. b) It is possible the conclusion of the test in part (a) is incorrect (contradicts with the reality). If this is the case, what type of error was made? Type I Error Type III Error Type II Error A…5.The following table summarized the age and blood pressure status of 474 randomly selected Canadian adults in 2017. At the 10% significance level, do the data provide sufficient evidence to conclude that age and blood pressure are associated?Suppose that 80% of 3–4-year-old children and 70% of5–8-year-old children in a village are vaccinated with QIVvaccine. Also assume that children who are not vaccinatedhave twice the incidence of influenza as the control groupin Table 3.7.3.29 What % of 3–4-year-old children in the village will getinfluenza?3.30 What % of 5–8-year-old children in the village will getinfluenza?3.31 Suppose we identify a 5–8-year-old child with influenzain the village but are uncertain whether the childwas vaccinated. If we make the same assumptions as inProblems 3.29–3.30, then what is the probability that thechild was vaccinated? (Hint: Use Bayes’ rule here.)
- The manager of a company that assembles and exports a particular type of pumps wants to know if there is a link between the number of hours spent by assembly workers in training and their productivity on the job. A random sample of 7 assembly workers was selected and their performances evaluated. The summary of the obtained data is listed in Table 2. Table 2: Shows the time spend by workers during training and their productivity on jobTraining hours (x) 20 36 20 38 40 33 32Output (y) 40 70 44 56 60 48 62 (i) Construct a scatter plot of the sample data and comment on the relationship between hours of training and output. (ii) Estimate a simple regression line, using the method of least squares, to identify a linear relationship between the hours of training received by assembly workers and their output (i.e. number of units assembled per day). (iii) Interpret, in context, the gradient/slope of the regression line. (iv) Estimated the output at 20 hours training time. (v) Interpret the…A low-level CDC bureaucrat wants to please his boss by gathering evidence thatthe current government-mandated shutdown of society is not causing people’s mentalhealth to deteriorate, so that it can safely be continued for several years if anyexpert says it’s necessary.He polls a random sample of 1600 citizens, gathering data on such items asincome loss, weight gain, access to toilet paper, hours spent binge-watchingNetflix, and number of injuries caused by household fights, and compiles all thisinto a scientifically-weighted “misery index”.The mean misery index from the sample is 99.2; it seems reasonable to use apopulation standard deviation σ = 19.1.a) Does this information provide significant evidence (at the 5% level) that thenationwide mean misery index is less than 100? Set up appropriate null andalternative hypotheses, calculate the appropriate test statistic, find the P-value,and state your conclusion. (10)b) A CDC press release publishing the results of this study claims that…A low-level CDC bureaucrat wants to please his boss by gathering evidence thatthe current government-mandated shutdown of society is not causing people’s mentalhealth to deteriorate, so that it can safely be continued for several years if anyexpert says it’s necessary.He polls a random sample of 1600 citizens, gathering data on such items asincome loss, weight gain, access to toilet paper, hours spent binge-watchingNetflix, and number of injuries caused by household fights, and compiles all thisinto a scientifically-weighted “misery index”.The mean misery index from the sample is 99.2; it seems reasonable to use apopulation standard deviation σ = 19.1.a) Does this information provide significant evidence (at the 5% level) that thenationwide mean misery index is less than 100? Set up appropriate null andalternative hypotheses, calculate the appropriate test statistic, find the P-value,and state your conclusion. b) A CDC press release publishing the results of this study claims that…