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#1
10-17-2010
 USMLE Forums Addict Steps History: 1 + CK Posts: 137 Threads: 49 Thanked 120 Times in 51 Posts Reputation: 140
95% Confidence Interval Question

A new treatment for elecated cholesterol is piloted on a sample of 100 men, ages 45-69 with total serum cholesterol in the range of 260-299 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. 210-290 mg/dL
B. 230-270 mg/dL
C. 246-254 mg/dL
D. 248-252 mg/dL
E. 249-251 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
10-17-2010
 USMLE Forums Veteran Steps History: 1 + CS Posts: 209 Threads: 34 Thanked 92 Times in 30 Posts Reputation: 122

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
 The above post was thanked by: atr88 (10-17-2010), Dr. N Elham (10-22-2010), Mondoshawan (05-13-2011)
#3
05-12-2011
 USMLE Forums Scout Steps History: 1 + CK Posts: 91 Threads: 17 Thanked 108 Times in 37 Posts Reputation: 118

Quote:
 Originally Posted by ecgram 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
can you explain again please, I'd choose B also; since it's 95% then it's 2 standard deviations below and above the mean, isn't ?
250 +/- 20 ??

#4
05-12-2011
 USMLE Forums Addict Steps History: 1+CK+CS Posts: 112 Threads: 20 Thanked 128 Times in 39 Posts Reputation: 143

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 (z-score) * 2 (SE) = 250 +/- 4

So CI will be 246 - 254 which is answer C

Hope this clarifies it
 The above post was thanked by: mle guy (05-13-2011), Mondoshawan (05-13-2011), USMLE-Syndrome (05-20-2011)
#5
05-13-2011
 USMLE Forums Scout Steps History: 1 + CK Posts: 91 Threads: 17 Thanked 108 Times in 37 Posts Reputation: 118

Quote:
 Originally Posted by drmuh 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 (z-score) * 2 (SE) = 250 +/- 4 So CI will be 246 - 254 which is answer C Hope this clarifies it

Oh thank you so much, I got it now
#6
05-13-2011
 USMLE Forums Master Steps History: Step 1 Only Posts: 919 Threads: 134 Thanked 1,325 Times in 364 Posts Reputation: 1348

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
05-13-2011
 USMLE Forums Master Steps History: 1+CK+CS Posts: 590 Threads: 31 Thanked 1,233 Times in 411 Posts Reputation: 1257
upp - be careful!

Quote:
 Originally Posted by Seetal 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!

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...
 The above post was thanked by: 1TA2B (05-14-2011)
#8
05-13-2011
 USMLE Forums Master Steps History: Step 1 Only Posts: 919 Threads: 134 Thanked 1,325 Times in 364 Posts Reputation: 1348
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 210-290 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:
 The above post was thanked by: Mondoshawan (05-13-2011)
#9
05-13-2011
 USMLE Forums Scout Steps History: 1 + CK Posts: 91 Threads: 17 Thanked 108 Times in 37 Posts Reputation: 118

Quote:
 Originally Posted by Seetal 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 210-290 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:

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
05-13-2011
 USMLE Forums Addict Steps History: 1+CK+CS Posts: 112 Threads: 20 Thanked 128 Times in 39 Posts Reputation: 143

I dont know the reason to choose B , the mistake can be to choose A (210-290) 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 200-300 mg/dl thats a much less valuable information than a 95\$ of the poulation cholesterol levels is from 245-255 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; 05-13-2011 at 09:10 AM.
 The above post was thanked by: mle guy (05-13-2011), Mondoshawan (05-13-2011), Seetal (05-13-2011), tinhi (05-13-2011)
#11
05-19-2011
 USMLE Forums Master Steps History: 1+CK+CS+3 Posts: 1,357 Threads: 194 Thanked 3,269 Times in 881 Posts Reputation: 3279

Quote:
 Originally Posted by drmuh I dont know the reason to choose B , the mistake can be to choose A (210-290) 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 200-300 mg/dl thats a much less valuable information than a 95\$ of the poulation cholesterol levels is from 245-255 mg/dL for example. And this why the larger the studies its results are more trusted than results of the smaller ones
we are talking about 95%CI!!!!...you should not concluded that "the 95% of the population cholesterol level calculated depending on the study was 200-300 mg/dl" nor that "95% of the poulation cholesterol levels is from 245-255 mg/dL for example"...
 The above post was thanked by: Claus_CU (06-09-2011)

 Tags Biostatistics-Epidemiology, Step-2-Questions

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