Use the given information to find the number of degrees of freedom, the critical values chi Subscript Upper L Superscript 2 and chi Subscript Upper R Superscript 2, and the confidence interval estimate of sigma. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Platelet Counts of Women 99% confidence; nequals23, sequals65.4.
Solution:
n=23
s=65.4
confidence level=0.99
alpha=0.01
alpha/2=0.01/2=0.005
1-alpha/2=1-0.005=0.995
df = n- 1=23-1=22
99% confidence interval for standard deviation is
sqrt(n*s^2/chisqupper<sigma<sqrt(n*s^2/chisqlower)
chisqupper in excel
=CHIINV(0.005,22)
= 42.79565
chilower in excel is
=CHIINV(0.995,22)
= 8.642716
99% confidence interval for standard deviation is
sqrt{(23-1)*65.4^2/42.79565)<sigma<sqrt{(23-1)*65.4^2/8.642716)
46.891<sigma<104.343
99% lower limit for standard deviation is 46.891
99% upper limit for standard deviation is 104.343
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