Question

Notice (from the margin of error measurment determined in 3b) that we have used a sample size larger than needed in order to be sufficiently confident that the sample mean would estimate the population mean height within 4 cm; that is our margin of error at 2.17 cm was much smaller than 4 cm. Therefore, determine the smaller sample size required to predict the mean height of all FHSU stats students based upon a needed 95% confidence level with an error of no more than 4 cm. (Again assume σ = 10.2 cm.)

Answer 1

the required sample size=n=25

here σ=10.2, confidence level=95%, so level of significance=alpha=100%-95%=5%=0.05, z(alpha/2)=z(0.05/2)=1.96

with (1-alpha)*100% confidence the margin of error=z(alpha/2)*sd/sqrt(n)

with 95% confidence the margin of error =1.96*10.2/sqrt(n)

or, 1.96*10.2/sqrt(n)=4

or, sqrt(n)=1.96*10.2/4

or, sqrt(n)=4.998

or, n=4.998*4.998=24.98 ( nearest whole number is 25)

answer is 25