Reference no: EM132268956
Questions - Read all questions carefully and submit your solution in a word file (NO PDF).
Q1. For the following abstracts, state the objectives/goals of the study and write analysis hypotheses (null and alternate) in words that are required to perform the hypothesis testing.
a. Early high school start times (EHSST) may lead to sleep loss in adolescents ("teens"), thus resulting in higher crash rates. In this study, we examined two other adjacent Virginia counties for the two years subsequent to the above-mentioned study. We again hypothesized that teens from jurisdictions with EHSST (versus later) experience higher crash rates.
(Vorona RD, Szklo-Coxe M, Lamichhane R, Ware JC, McNallen A, & Leszczyszyn D. Adolescent crash rates and school start times in two central Virginia counties, 2009-2011: a follow-up study to a southeastern Virginia study, 2007-2008. J Clin Sleep Med 2014;10(11):1169-1177.)
b. Sleep problems can occur at any age. Inadequate sleep affects the physiological as well as psychological well-being of an individual. Thus, the objective of the present study is, to determine the pre sleep habits, duration and pattern of sleep among school children and to determine association between their sleep schedules and sleep habits.
(Mishra, A., Pandey, R. K., Minz, A., & Arora, V. (2017). Sleeping Habits among School Children and their Effects on Sleep Pattern. Journal of caring sciences, 6(4), 315-323. doi:10.15171/jcs.2017.030).
c. Obesity and type 2 diabetes continue to increase in prevalence in the U.S. Whether diabetes incidence continues to increase in recent times is less well documented. We examined trends in diabetes incidence over the previous four decades.
(Abraham, T.M., Pencia, K.M., & Fox C.S.(2015). Trends in diabetes incidence: The Framingham Heart Study. Diabetes Care,38(3),482-487.)
Q2. Define the null and alternate hypotheses and identify if it is one tail or two tail test. (Use standard notation such as H0: ..... Do not use word statements, for example H0: µ=20 vs H1: µ ≠ 20, two tail test).
a. Mr. A claimed that average age of pregnant women is 27 years.
b. It is known that average amount of time a college student spends on cell phone is more than 2.8 hours per day.
c. A poultry farm claimed that the average weight of chicken in his farm is at least 5 lbs.
d. It is assumed that the average minimum wage can't exceed $9.50.
e. Percentage of students with grade 'A' is more than 30%. (Use p as notation for population proportion)
f. Percentage of smokers in the rural area is 33%.
Q3. For the following confidence intervals, calculate the margin of errors (ME) and best estimate of unknown characters of the population.
a. Confidence interval for average height of Virginia adults is (5.65, 6.25) inches.
b. CI for percentage of death from breast cancer in the US is (1.1, 4.1).
Q4. What happens to the CI when we increase the ME, will it increase or decrease?
Q5. How do you interpret "90% CI of population mean is (12.5, 15.1)"?
Q6. We drew two samples of same size from the same population and 95% CI were calculated.
Sample 1-95% CI of µ is (23.5, 26.5).
Sample 2-95% CI of µ is (22.5, 29.3).
If you have to consider one sample for the analysis, which one do you prefer and why?
Q7. In which of the following conditions, we reject the null hypothesis?
a. p-value > level of significance (α)
b. CI contains the value from the null hypothesis.
c. p-value < α
d. CI does not contain the value from the null hypothesis.
Q8. We are performing hypothesis testing on
H0: 20 where α = 0.10.
H1: 20
a. If the p-value =0.08, do you reject or fail to reject the H0? Why?
b. What will be the confidence level of this test?
c. If the calculated 90% confidence interval of µ is (20.5, 25.5). Do you reject or fail to reject the H0? Explain.
d. If the calculated 90% confidence interval of µ is (15.5, 19.5). Do you reject or fail to reject the H0?
e. Will the 95% CI be wider or narrower than 90% CI?
f. Interpret the meaning of 90% confidence level of any population parameter?
Q9. 85 arrested people were sent to the court and the judgement was made as follows.
|
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Actual Status
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|
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Innocent
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Criminal
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Criminal
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2
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71
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Innocent
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7
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5
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Before making any decision, it was assumed that everyone was innocent.
What is the false positive error in this case? What is the rate of false positive (α). False positive rate is also called Type I error rate.