Can someone help me with this? Suppose we make five measurements of a quantity w

Question

Can someone help me with this?

Suppose we make five measurements of a quantity we know to be normally distributed with mean 0.05. We obtain 0.041, 0.064, 0.055, 0.046, 0.060. a) Estimate the variance of the distribution. b) Suppose we know that the variance is, in fact, 5.0 times 10^- 5. What is the value of chi^2 for this set of measurements? c) What is the "p value, " i.e. the right-tail integral, for this value of chi^2? d) Suppose that indeed we knew the variance of the underlying Gaussian to be 5.0 times 10^-5 but did not a priori know the mean. Under these circumstances what p value would we obtain?

Explanation / Answer

a) Using Excel function =VAR(0.041,0.064,0.055,0.046,0.06)

we get the variance s^2=0.0000917

b) Chi-square=(n-1)*s^2/sigma^2

=(5-1)*0.0000917/0.00005

=7.336

c) Degree of freedom=n-1=5-1=4

p-value=0.1192/2=0.0596 using excel function =CHIDIST(7.336,4)

d) In this case p-value remains the same as mean has no role to play in this test

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