Question

Let X1,....,XN be a random sample from N(Mu, sigma squared). Both parameters unknown.

a) Give two pivotal quantities based on the sufficient statistics and determine their distribution functions. The best solutions are those you can use to construct confidence intervals for Mu and sigma squared.

b) If a random sample of size 5 is observed as follows: 9.67, 10.01, 9.31, 9.33, 9.28, find a 95% equal tailed confidence interval for sigma squared.

c) Based on the above observations, find a 95% equal tailed confidence interval for Mu.

Answer 1

a) The two pivotal quantities that can be used to construct a confidence interval for population mean and variance is sample mean and sample variance.

b) the mean and standard deviation of the given sample is

the 95% confidence interval for sigma squared is

for 95% confidence and df= n-1

critical values:

c) 95 % confidence interval for men is

for 95% . confidence and df= n-1=5-1=4