Practice problem set part2 1. Researchers are interested in conducting an observational study investigating the relationship between hepatitis C and early mortality in HIV positive patients. The following table represents the findings from the study after a follow-up time period of 15 years. Hepatitis C + Hepatitis C Total Decease d 421 Not Deceased 348 Total 425 846 820 1168 1245 2014 769 A) Calculate the mortality rate in the exposed and unexposed. B) Is mortality a measure of incidence or prevalence? Ans: A) 0.5475. 0.341 B) Incidence Pg. 396 The formula depends on two factors, parameter of interest and sample size(s). Given a question write down each of these in the context f the problem. 2. Recently there has been a marketing push promoting the new wave of electronic cigarettes in the media. Suppose a new study claims that those that they have determined that e-cigarette smokers still have a much higher risk for esophageal cancer than nonsmokers. Assume the following table of summary statistics describes the SRSs of those in the e-cigarette group versus non-smokers. Study Group E-cigarette Smokers Non-Smokers Average # of cases of esophageal cancer 21.4 2.7 Standard deviation Sample Size 1.8 0.8 749 898 A) Carry out a two sample independent test of hypothesis to determine if there is a significant difference in the number of esophageal cancer cases in e-cigarette smokers versus nonsmokers. Use an alpha level of 0.05. Use the pooled variance calculation under the equal variance assumption. parameter of interest = 1 - 2 , where 1. 2 are the mean # of esophageal cancer cases among e-cigarette smokers and nonsmokers respectively. Sample sizes- 749 and 898 (both large). Choose the appropriate Ha next (<, or >) Ho: 1 - 2 = 0 1 - 2 0 Test statistic 21 n1 + 22 ) n2 x 1 x 2D0 Z= ( 2 1.8 749 +0.82 ( ) 898 21.42.70 = B) Construct a 99% confidence interval for the difference in number of esophageal cancer cases between the groups. Plug in the values to the following formula 2 1 n1 + 22 x 1x 2 ( ) n2 z 1 Note z 1 2 2 = Z.995 =99.5th percentile= 2.57 Ans: A) Ho: 1-2=0 Ha: 1-2 0 Z statistic =263.45 Pvalue~0 Reject your Ho that there is no difference in esophageal cancer cases between exposure groups. B) (18.569, 18.831) - approximately due to round off Pg. 275 3. Recent publications have hinted at the growing importance of sleep in the elderly in order to maintain good health. Suppose a researcher is interested in the hypothesis that the difference in average hours of sleep differs significantly between men aged 35-45 and men aged 45+. Assume the following table summarizes the descriptive statistics for SRSs from each age group. Carry out the appropriate statistical test to answer the researcher's hypothesis regarding the difference in average hours of sleep between the two groups under investigation. Assume that all conditions for the testing are met. Use an alpha level of 0.05. Calculate a pooled variance under the equal variance assumption. Write out your null and alternative hypotheses and interpret your pvalue. Age group 35-45 45+ Ans: Average hours of sleep 7.4 5.2 Standard deviation Sample Size 1.02 0.87 24 32 A) Ho: 1- 2 =0 Ha: 1- 2 0, 1, 2 are the mean # of sleep hours for 35-45 age group and 48+ group respectively. T statistic=8.697 Pvalue=7.53*10-12 Reject the Ho that there is no significant difference in average hours of sleep between the two age groups being compared. Pg. 275 4. Researchers at a local public health office are interested in the difference in prevalence of sickle cell anemia by ethnicity in a population under its jurisdiction. Suppose the following table represents prevalence of sickle cell anemia reported based on a thorough survey. Ethnicity AfricanAmerican Other Prevalence of Sickle Cell =242/1049 =165/1864 A) Calculate the risk difference between the groups. B) Conduct a formal test to determine if there is a significant difference in the prevalence of sickle cell anemia between the two groups. Write out your null and alternative hypotheses and interpret your results. Use an alpha level of 0.05. Ans: A) risk difference=0.1422 B) Ho: p1-p2 =0; Ha: p1- p2 0, where p1, p2 are Prevalence of Sickle Cell in AfricanAmericans and other ethnicities respectively. Z stat=10.6 Pvalue = 2.3*10-26 ~ 0 Reject the Ho that the proportions are assumed equal. Infer that the proportion of sickle cell anemia among African Americans is likely to be larger than other races. Pg. 430 5.Researchers at an epidemiology clinic have conducted a study investigating the relationship between exposure to asbestos and lung cancer. The following table represents the findings from the study after a follow-up period of 10 years. Asbestos Exposure + Asbestos Exposure Total Lung Cancer 153 No Lung Cancer 201 Total 23 176 664 865 687 1041 354 A) Calculate the proportion of lung cancer cases in both the exposed and unexposed. B) Are these incident or prevalent cases of lung cancer? Ans: A) Exposed=0.4322, un-exposed=0.0335 B) incident Pg. 396 6.A research team is hired to investigate the prevalence of periodontal disease in a rural county with a low average socio-economic status. The team is given the task of surveying the area, and providing a brief examination of participants to correctly identify cases of periodontal disease and estimate an overall prevalence. If the team identifies an overall prevalence of above 25%, the sponsoring organization is to initiate an active campaign promoting healthy dental practice. Out of 2,879 participants surveyed, 589 were identified to have periodontal disease. A) Conduct a formal test for detecting if the prevalence of periodontal disease among the residents in this rural county with a low average socio-economic status is significantly different from the minimum prevalence for intervention. Use an alpha level of 0.01. B) Interpret your conclusions. Ans: A) Ho: p=0.25, Ha: p0.25, where p= the prevalence of periodontal disease among the residents in this rural county with a low average socio-economic status. Z statistic=-5.6257 Pvalue=<0.0001 C) The proportion of the periodontal disease among the residents in this rural county with a low average socio-economic status is significantly different from the prevalence threshold. Intervention plans should not be made (b/c the negative sign of the Z statistic indicates that the prevalence for this low income group is less than .25. This is also indicated from the sample proportion p = 589/2879 = .204 being smaller than .25. Note that intervention is recommended if prevalence is more than .25. Alternatively (and preferably), a one tailed hypothesis can be carried out with Ho: p=0.25, Ha: p >0.25, Then Z=-5.6257 (same as in part A) with p-value for Z=5.6257 to be almost 1 (=1-0.0000000) as shown in the Minitab result below Cumulative Distribution Function Normal with mean = 0 and standard deviation = 1 x -5.6257 P( X x ) 0.0000000 Z= -5.6257 p-value for right tailed test= probability to the right of the test statistics (z=-5.6257) = 1-0.0000000 =1 This large p-value indicates that Ha should be rejected which means that we cannot accept that prevalence in the low-income group is nt more than 0.25. Therefore intervention plans are not recommended. p-value= 1=1-0.00000000. Pg. 403