Reference no: EM132285081

Assignment - Inference on Qualitative Data

Read all questions carefully and submit your solution in a word file with R outputs (NO PDF).

Q1. In a sample of 45 individuals, it was found that 15 were left handed. Test the hypothesis that right handed population is at least 30% more than left handed population. Show all 5 steps: Define null and alternative hypothesis, determine the level of significance, test-statistic value from the R output, p-value, and conclusion with R outputs.

Q2. A group of researchers identified 500 individuals with esophageal cancer based on a questionnaire given to patients at a nearby hospital. These patients were compared to a group of 500 individuals who reported no history of esophageal cancer. In the questionnaire, both groups were asked if they smoke or have ever smoked. The prevalence of smoking was 33% among the esophageal cancer group and 14% among the group with no history of esophageal cancer.

a) Is this cohort or case-control study?

b) Perform a hypothesis testing to see if the proportion of esophageal cancer in smoker group significantly different from that of never smoked group. Show all 5 steps: Define null and alternative hypothesis, determine the level of significance, test-statistic value from the R output, p-value, and conclusion with R outputs.

c) Calculate OR and interpret it. Is OR significant? Explain. Interpret the CI of OR.

d) What is RR for this example?

Q3. In 1982 The Physicians' Health Study (a randomized clinical trial) was begun in order to test whether low-dose aspirin was beneficial in reducing myocardial infarctions (heart attacks). The study population consisted of over 22,000 male physicians who were randomly assigned to either low-dose aspirin or a placebo (an identical looking pill that was inert). They followed these physicians for about five years. Some of the data is summarized in the 2x2 table shown below.

a) Is this cohort or case-control study?

b) Calculate the RR, and OR and interpret them.

c) Are RR and ORs significant? Interpret the confidence intervals of RR and OR.

d) What is the AR of treatment? Interpret it. What is AR%? Interpret the AR%.

Q4. Low socioeconomic status (SES) children perform on average worse on intelligence tests than children from higher SES backgrounds, but the developmental relationship between intelligence and SES has not been adequately investigated (Stumm & Plomin, 2015). In this problem we want to test whether there is any association between intelligence and economic conditions. In a college, 1,072 students were classified according to their intelligence and economic conditions.

Perform a hypothesis testing to see whether there is any association between intelligence and economic conditions. Show all 5 steps: Define null and alternative hypothesis, determine the level of significance, test-statistic, p-value, conclusion with R outputs.

Reference: von Stumm, S., & Plomin, R. (2015). Socioeconomic status and the growth of intelligence from infancy through adolescence. Intelligence, 48, 30-36. doi:10.1016/j.intell.2014.10.002.