We have seven observations drawn independently from a normal

We have seven observations drawn independently from a normal distribution with unknown mean mu and variance sigma^2. You are trying to test the hypothesis H0 : mu = 25. You can use the enclosed normal and t-tables. (a) Estimate mu and sigma^2 if the observations are 30.2413 26.9571 28.8098 31.5834 30.8127 29.4452 33.1271. (b) An oracle told you that sigma = 2. Test the null hypothesis at 5% significance level.

Solution

a)mean=30.1391

var=3.9752

b) since sigma is known we use z test.

z=xbar-mu/s/sqrt(n)

p<0.05, we reject H0.

25.000000	hypothesized value
30.139500	mean label
1.993800	std. dev.
0.753586	std. error
7	n
6.82	z
9.10E-12	p-value (two-tailed)