A researcher wants her sample mean to be twice as accurate; how much does she ha

Question

A researcher wants her sample mean to be twice as accurate; how much does she have to increase her sample size by? An article in the New England Journal of Medicine reported that among adults living in the United States, the average level of albumin in cerebrospinal fluid is 29.5 mg/dl, with a standard deviation of 9.25 mg/dl. We are going to select a sample of size 20 from this population. How does the variability of our sample mean compare with the variability of albumin levels in the population? What is the probability that our sample mean will be greater than 33 mg/dl? What is the probability that our sample mean will lie between 29 and 31 mg/dl? What two values will contain the middle 50% of our sample means?

Explanation / Answer

a)std error of mean =std deviation/(n)1/2 =2.0684

b)P(X>33)=1-P(X<33)=1-P(Z<(33-29.5)/2.0684)=1-P(Z<1.6922)=1-0.9547=0.0453

c)P(29<X<31)=P(-0.2417<Z<0.7252)=0.7658-0.4045=0.3613

d) for middle 50% values ; z=+/- 0.6745

hence corresponding values =mean +/- z*std error =28.1049 ; 20.8951

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