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#1




95% Confidence Interval Question
A new treatment for elecated cholesterol is piloted on a sample of 100 men, ages 4569 with total serum cholesterol in the range of 260299 mg/dL at entry. Following 3 months on the medication, the mean cholesterol for the treatment group was 250 mg/dL with a standart deviation of 20 mg/dL. What is the 95% confidence interval on the mean for the study?
A. 210290 mg/dL B. 230270 mg/dL C. 246254 mg/dL D. 248252 mg/dL E. 249251 mg/dL Keeping in mind that the mean is 250 mg/dL and that the standart deviation is 20, two standard deviations above and below the mean will lead us to 95% confidence interval, I selected option B, however, the right answer is C. Could somebody explain why I'm wrong? 
#2




yeaaa C is correct answer the formula for the confidence interval is mean+ or  Z score XSD/square root of n
so mean is 250, Z score for 95 % is 2 ,SD given 20 and square root of 100 which is n is 10 so if u do the calculation u will ger 250+ or  4 which is C hope u understood 
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#3




Quote:
250 +/ 20 ?? 


#4




CI = Mean +/ z score * SE ( Standard error not SD)
z score for 95% = 2 SE = SD / square root of n Now you can apply on the above question: n = 100 SE = 20 (SD)/ square root of 100 (n) = 20 /10 = 2 CI= 250 (mean) +/ 2 (zscore) * 2 (SE) = 250 +/ 4 So CI will be 246  254 which is answer C Hope this clarifies it 
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#5




Quote:
Oh thank you so much, I got it now 
#6




ok i get ur formula. but when 95% CI is 2 SD above and below the mean, without using the formula, shouldn't we pick A as the answer? y did u pick B without the formula? 2 SDs means 40mg now instead of 20mg ryte?
on another note... thx for the formula n the question! 
#7




upp  be careful!
Quote:
95% being 2 SD above or below the mean is a description of the area under a normal curve  not CI. For CI you need to use the formula described by drmuh and ecgram. It makes sense, too, right? How much confidence you have in the result of a study will to some extent be a function of the sample size... 
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1TA2B (05142011) 
#8




thts not what i meant.
i understand tht for the 95% CI we need to use the formula.
now lets say the 95% CI was not given but the value of SD being 20mg was given. then for 2 SDs u would have a value of 210290 ryte? sigh... .. im confusing everyone now....hang on.. let me be more clearer.... y did Dr. N Elham choose answer B at first? how did u reach tht answer before the formula came up?.. in other words.. forget about the formula here, tell me how you got B? :sorry: 
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Mondoshawan (05132011) 
#9




Quote:
so we did a double mistake it's true B is not the answer at all I calculated like 2 SD, but instead of 20; I've used 10!! 
#10




I dont know the reason to choose B , the mistake can be to choose A (210290) using the 2 SD issue.
Why its wrong to use SD is that we are dealing with a random sample and we need to use a deviation parameter corrected to the size of the sample we have; which is called the SE. Another issue in this formula is the effect of the sample size. in case of larger random sample ( n large), the SE will be low, and the CI will be narrow and more precise. Now in case the random sample is small (n small), SE will be high, and the CI will be wide and less precise. For example in the example above assume the 95% of the population cholesterol level calculated depending on the study was 200300 mg/dl thats a much less valuable information than a 95$ of the poulation cholesterol levels is from 245255 mg/dL for example. And this why the larger the studies its results are more trusted than results of the smaller ones Last edited by drmuh; 05132011 at 10:10 AM. 
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#11




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Claus_CU (06092011) 
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BiostatisticsEpidemiology, Step2Questions 
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