The mean and standard deviation of a random sample of n measurements are equal t

Question

The mean and standard deviation of a random sample of n measurements are equal to 34.8 and 3.6, respectively. a. Find a 99% confidence interval for mu if n = 100. b. Find a 99% confidence interval for mu if n = 400. c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed? a. The 99% confidence interval for mu if n = 100 is approximately (Round to three decimal places as needed.)

Explanation / Answer

a) for n=100; std error=std deviation/(n)1/2 =0.36

for 99% CI, z=2.5758

hence 99% COnfidence interval = mean -/+ z*std deviation =33.8727 ; 35.7273

b)

for n=400; std error=std deviation/(n)1/2 =0.18

for 99% CI, z=2.5758

hence 99% COnfidence interval = mean -/+ z*std deviation =34.3364 ; 35.2636

c) width for part a) =z*std deviation =0.9273

width for part b) =z*std deviation =0.4636

width decreases by half od quadrupling the sample size,.

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