Question

e) If the Paint manufacturer would like to estimate the population mean life of the paint before corrosion occurs. He wants to be 90 % sure of his estimate and he wants his estimate to be within 3 hours of the population mean. Suppose he does not know the population standard deviation and hence decides to select a pilot sample of 40 panels and finds the sample standard deviation to be 20 hours. How many more panels does the manufacturer need to select as part of his sample so as to expose them to various corrosive conditions to measure the protective ability of the paint?   

Answer 1

given that

level of significance=90%

margin of error=ME=3

panel sample size=k=40

sample standard deviation=S=20

since here sample size greater than we will use Z statistics

now let required sample size is "n" then

this gives

so n~121

number of more panels needed =121-40=81

so 81 more panels needed.