Question

question 7b is confusing

trying to determine the melting point of a new material, of which you have a large number of samples. For each sample that you measure you find a value close to the actual melting point c but corrupted with a measurement error. We model this with random variable Mi = c + Ui where Mi is the measured value in degree Kelvin, and Ui is the occurring random error. It is known that E(U;) = 0 and Var(U) 3, for each i, and that we may consider the random variables Mı, M2,.. independent 7. You are (a) According to Chebyshev's inequality, how many samples n do you need to measure to be 95% sure that the average of the measurements is within half of degree of c (b) Assume that the random errors Ui in the measurements have a normal distribution, find a less conservative value for n you need to measure to be 95% sure that the average of the measurements is within half of degree of c 8. In the final of the World Series Baseball, two teams play a series consisting of at most seven games

Answer 1

7b) For the mean the margin of error is given by

Moe a/2

Where for 95% confidence level, the critical value ​​​​​​

a/2=1.96

Also its given that ​​​​​​

Moe 0.5 aV

Using these values we get the sample size required n as

V3 0.5 1.96 Vn Vn 3.923 n46.10

So sample size required is 47