Consider a random sample of ten children selected from the population of infants

Question

Consider a random sample of ten children selected from the population of infants receiving antacids that contain aluminum. The distribution of plasma aluminum levels is known to be approximately normal; however, its mean µ and the standard deviation are not known. The mean aluminum level for the sample of ten infants is x = 37.2 µg/l and the sample standard deviation is s = 7.13 µg/l.

a) Use the t distribution to find 95% confidence limits for µ

b) What would the 95% confidence interval be if the population standard deviation was known to be equal to the sample value of7.13 µg/l?

Explanation / Answer

here std error =std deviation/(n)1/2 =2.2547

and for 95% CI and 9 degree of freedom t=2.2622

hence confidence interval =mean +/- t*Std errror =32.0995 ; 42.3005

b) if its known then z =1.96

and confidence interval =mean +/- z*Std errror =32.7809 ; 41.6191

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