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Hypothesis testing is one of the mainstays of medical research literature. You would be hard-pressed to find a research article in a clinical journal that doesn't contain the results of at least one hypothesis test. So it's important to think critically about hypothesis tests and what they mean--what they can and can't tell us about our data. I've presented three situations below. Write up a brief description of the problem with the conclusion drawn from the hypothesis test. Note that the problem is not in the calculations--assume the calculations are correct--but in the interpretation of the test.
1. In an observational study of the effect of a physician quality reporting system, the mean age of the patients of physicians participating in the program is 72.675 years, while the mean age of the patients of physicians not participating in the program is 72.950 years. The total sample size is nearly 11,000 patients. The p-value for the hypothesis test that the mean ages are different is 0.001 (Null hypothesis: the difference in mean ages of the two groups is zero; alternative hypothesis: the difference in means is greater than or less than zero). The analyst concludes that the patients of physicians not participating in the program are older than the patients of participating physicians and therefore not a good comparison group for an observational study.
2. A 1999 study looked at the effect of exposure to perchlorate on rats' thyroids. 30 rats were exposed to perchlorate and their thyroids were compared to 30 rats not exposed to perchlorates. Two of the rats exposed to perchlorate were found to have a rare type of thyroid tumor. Zero of the rats not exposed to perchlorate had tumors. The experimenters performed a hypothesis test for the difference in number of tumors and got a p-value of 0.48. They concluded that perchlorate exposure does not cause thyroid tumors in rats.
3. Three psychiatrists studied a sample of schizophrenic and non-schizophrenic people. They measured 77 variables for each subject - religion, family background, childhood experiences etc. They wanted to determine what factors cause people to later become schizophrenic. Using their data they ran 77 hypothesis tests of the significance of the differences between the two groups of subjects, and found 2 significant at the 2% level. They immediately published their findings.
The City Transit Authority plans to hire 8 new bus drivers. From the group of 100 qualified applicants, of whom 55 are men and 45 are women, 8 names are to be selected by lot. Suppose that Mary and John Lewis are among the 100 qualified applicants..
Tthe United States during 1993 was $40,500. Assume the standard deviation was $8,500. Should a mobile home selling for $75,000 be considered an outlier? Explain why or why not.
question the bank customer waiting time caserecall that a bank manager has developed a new system to reduce the time
Determine the mean and the standard deviation of the sample.
At the 5 percent level of significance, can we conclude that the mean weight is greater than 16 ounces? Determine the p- value.
Critically discuss the reasons for studying statistics? Choose five random numbers between 70-100. Calculate the mean, and midrange of these numbers.
Rewrite this simplified radical form. Assume all variabel represent positive real numbers.
If a six appears for the second time, the process is repeated with the move depending on the number shown and the previous throws. If a six appears for the third time, the turn of the player ends without moving the token.
You are working on an analysis of your company's current cost structure reviewing the various fixed and variable costs within your firm. Your objective is to maximize your firms profit.
1.at what age do babies learn to crawl? does it take longer to learn in the winter when babies are often bundled in
Jamie expects that a bulb will last for 400 to 500 days, what is the probability of an Acme bulb satisfying that?
Of 970 subjects, 20 answered yes and 950 answered no. find p^, the proportion of the sample who were victims. Find the standard error of this estimate.
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