23. The following are body mass index (BMI) Scores measured in 12 patients who a

Question

23. The following are body mass index (BMI) Scores measured in 12 patients who are free of diabetes and are participating in a study of risk factors for obesity. Body mass index is measured as the ratio of weight in kilograms to height in meters squared. To calculate a 95% confidence interval estimate of the true BMI, what is value for margin of error? (round to one decimal place) 25 27 31 33 26 28 38 4124 32 35 40 24. Based on the data provided in Q23, how many subjects would be needed to ensure that a 95% confidence interval estimate of BMI had a margin of error not exceeding 2 units?

Explanation / Answer

Step 1: Find the critical value. The critical value is either a t-score or a z-score. If you aren’t sure, see: T-score vs z-score. In general, for small sample sizes (under 30) or when you don’t know the population standard deviation, use a t-score. Otherwise, use a z-score.
So in this case n=12, critical value of t at 95% confidence with (n-1)=(12-1) d.f is 2.20

Step 2: Find the Standard Deviation or the Standard Error. These are essentially the same thing, only you mustknow your population parameters in order to calculate standard deviation. Otherwise, calculate the standard error.

sample standard deviation is 5.88

standard error= s/sqrt(n)= 5.88/sqrt(12)= 5.88/3.46= 1.7

Step 3: Multiply the critical value from Step 1 by the standard deviation or standard error from Step 2.

= 2.20*1.7= 3.74

Therefore margin of error is 3.74 = 3.7

95% confidence interval is

Mean = 31.67

t = 2.2
sM = (5.882/12) = 1.7

= M ± t(sM)
= 31.67 ± 2.2*1.7
= 31.67 ± 3.736

M = 31.67, 95% CI [27.9, 35.4.

You can be 95% confident that the population mean () falls between 27.9 and 35.4

24) Step 1: Find t a/2 by dividing the confidence interval by two, and looking that area up in the t-table for (n-1) d.f

.95/2 = 0.475 The closest t-score for 0.475 is 2.2 for 11 d.f

Step 2: Multiply step 1 by the standard deviation.
2.2* 5.88 = 12.94

Step 3: Divide Step 2 by the margin of error. Our margin of error (from the question), is 2.
12.94/2 = 6.47

Step 4: Square Step 3.
6.47*6.47= 41.86= 42 (approx)

sample size required is 42.

Like the explanation? Then thmbs up ;)

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