A hypothesis test if is set up as follows:

H1:

8 measurements give an average x = 3.83. It is known that = 0.9.

The test shall be performed with significance level = 0.5%.

a)

Determine critical value, k.

Round your answer to 2 decimal places.

b)

What is the strength of the test if H1: = 3.96 is true?

Round your answer to 4 decimal places.