a) How big must the sample be to estimate this age within +- 2 years with 95% co

Question

a) How big must the sample be to estimate this age within +- 2 years with 95% confidence? Assume that the range of patients represents 6*Sigma and the oldest patient they have had in recent months was 102 years old, then Sigma =102/6 =17 years. Use 17 years as an estimate of .

b) If a sample of that size is then obtained and the sample mean is Xbar=44 years old, then what is the desired confidence interval? Interpret the meaning of that interval.

c) Suppose you also obtain s=14.6 years from that sample. Using s=14.6 and n from (a) as well as the maximum error of +- 2 years, can you be more than 95% confidence that 42 < µ < 46, which should have been obtained in (b)? How? Why?

Explanation / Answer

a) here =17 ; margin of error E=2

for 95% CI ; z=1.96

therefore sample size n=(z*/E)2 =~278

b)for above margin of error =2

hence confidence interval =Xbar -/+ margin of error =42 ; 46

abvoe interval gives 95 percent confidence to contain true population mean age of patients

c)as std deviation estimated here is less then what we have in part b. there fore because of low variability we can be more than 95% confidence that 42 < µ < 46.

please revert for any clarification required

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