Question

Suppose the incidence rate of myocardial infarction (MI) was 5 per 1000 among 45- to 54-year-old men in 2000. To look at changes in incidence over time, 5000 men in this age group were followed for 1 year starting in 2010. Fifteen new cases of MI were found. Suppose that 25% of patients with MI in 2000 died within 24 hours. This proportion is called the 24-hour case-fatality rate.

1. Of the 15 new MI cases in the preceding study, 5 died within 24 hours. Test whether the 24-hour casefatality rate changed from 2000 to 2010.

2. Suppose we eventually plan to accumulate 50 MI cases during the period 2010–2015. Assume that the 24-hour case-fatality rate is truly 20% during this period. How much power would such a study have in distinguishing between case-fatality rates in 2000 and 2010–2015 if a two-sided test with signifcance level .05 is planned?

3. How large a sample is needed in question 2 to achieve 90% power?

Answer 1

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; Null hypothests : Hosp, plz. That is, there is no difference between the 24-hour rate carefatality changed from 2000 to 2olo, Alternative hypothesis : A BitP₂ - That is, there is a difference between the 24-houx care fatality rate changed from 2000 to 2010. Test statistics from the given information for the question can write, P = 25%, 0, 25, X = 5 4 22 215. 2. Pia 0.25. P2 = 2 = 5 15 =0,33 The poded sample proportion is, êxittle nitt. - 1580252+5 5+15, 0.3125, Zfest 0.25 - 0:33 Social (it) Jaanus (1-o. 308 (f + 1/2)

-0.08 0.239357 = -0.334, Criscal value & from the given information, the significance level is 0.05 that is, 2/2 2005/2. 20.025 from standard normal table, the corresponding on thal value is +1.96. decision rule, - IS - 1,962dest statistie 21,96 then do not reject the hell hypothests. + If the test stubiste <-1,96 on the test statistie 2196 then reject the hell hypothesis. condersion ! + The test statistic is 0.334, which is l'as between the cristal values of 196 and 1.96, from the decision rule, do not reject the null hypothesis. It can be concluded that there is no difference blo the 24-hour care fatality rate changed from 2000 to 2olo, every step is written clearly just read and understand the abore there worlt be steps detaily any we need to find power Power Z2g / PCLP (2 + 1 4 ) + CP (12) ✓ Perps ( 1 ) misunderstanding 3) P Z L

fram the given information, P.72506, 9128, P22 0.20 and m50. The pooled Sample proportion is, Pasith nit. = (5x0.25 3+C50x0,20) 5+50 02045, Power =P ZL 12 P 22J PC-P) (t + 1 2 ) + (P1-P2) v peop) (htt) z21,965 0.2045 (1-0.2015) (3 + 1/ / to. 0.2013) 6 to [2222243] 0.9869 (: from excel Junction, 0.2045 Cho:2048) Jo - NORM. DI&T (2.2243,0,1, TRUE) doubts. I everything is explained detaily in the above steps, go through those y you have any thank * kindly give upvote you & support my efforts