Consider a normal population distribution with an unknown mu and known standard

Question

Consider a normal population distribution with an unknown mu and known standard deviation sigma = 3 A confidence interval for w is given by the following formula. X bar - Za sigma/2/squareroot n less than or equal mu lessthanorequalto x bar + Za sigma/2/squareroot n What is the confidence level (Cl) for the interval x bar - 1.9 sigma/squareroot n lessthanorequalto mu lessthanorequalto x bar + 1.9 sigma/squareroot n Compute a 98% confidence interval for mu when n = 49 and x bar = 80 How much is the error associated with the 98% confidence interval for mu found in question 2? Find the sample size, n, for which the 98% confidence interval for has a maximum error of 0.7

Explanation / Answer

1) here for z=1.9 confidence level =94.26%

2)here std error =std deviation/(n)1/2=3/(49)1/2

for 98% CI, z=2.326

hence 98% confidence interval =sample mean -/+ z*std error =80 -/+2.326*3/(49)1/2 =79.003 ; 80.997

3)

error =z*std error =2.326*3/(49)1/2 =0.997

4)

here error E =0.7

std deviation =3

and for 98% CI; z=2.326

hence sample size n=(z*std deviation/E)2 =~100

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