Question 1170808: It is known that the weights of apples from a farm are normally distributed. In order to estimate the mean weight, a random sample of 150 apples is considered and the sample mean and population standard deviation are 6 kg and 0.8 kg respectively.
(a) Construct a 95% confidence interval estimate for the population mean weight of apples.
(b) The researcher suggests doing the study again so that 98% confidence interval estimate for the population mean weight of apples is (5.8835,6.1165) kg. How large should the sample size be?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! the half-interval is z(0.975)*sigma/sqrt(n)=1.96*0.8/sqrt(150)
=0.128, which is subtracted from and added to the mean
(5.872, 6.128) units kg
here, the error is 0.1165, and that equals z(0.99)*0.8/sqrt(n)
so 0.1165 *sqrt(n)=2.326*0.8=1.8608
divide both sides by 0.1165 and square the answer, which is 255.12 or 256 apples.
Because a lot of these problems don't round the z-value, which I have, I always go back on the calculator and do a CI check of both n=255 (closest) and n=256 (rounding up, conservative).
n=255 gives the answer exactly.
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