(a) Measurements of a known quantity are taken and the quanitity is normally dis

ID: 3232155 • Letter: #

Question

(a) Measurements of a known quantity are taken and the quanitity is normally distributed with mean 0.05. We obtain 0.041, 0.064, 0.055, 0.046, 0.060. Estimate the variance of the distribution.
(b) Suppose we know that the variance is, in fact 5.0 x 10^-5 . What is the value of the chi squared for this set of measurements?
(c) What is the "p value" for this value of chi squared?
(d) Supposed the variance of the underlying Gaussian is known to be 5.0 x 10^-5 but we didn't know the mean beforehand. Under these circumstances, what p value would be obtained?

Explanation / Answer

Answer:

Data x

x-0.05

(x-mean)^2

0.041

-0.009

0.000081

0.064

0.014

0.000196

0.055

0.005

0.000025

0.046

-0.004

0.000016

0.06

0.01

1E-04

Total

0.000418

Variance =0.000418/4=0.000105

Chi square= 4*0.000105/0.00005 =8.4

P=0.078

data

count

mean

0.05320

sample standard deviation

0.00958

sample variance

0.00009

Chi square= 4*0.00009/0.00005 =7.2

P=0.1257