Question

Suppose µ is the mean of a normally distributed population for which the standard deviation is known to be 3.5. The hypotheses H0 : µ = 10 Ha : µ 6= 10 are to be tested using a random sample of size 25 from the population. The power of an 0.05 level test when µ = 12 is closest to

Answer 1

Solution:

Given :µ is the mean of a normally distributed population for which the standard deviation is known to be 3.5. That is:

           Vs  

Sample size = n = 25

Level of significance = 0.05

We have to find Power of the test when µ = 12.

Power = 1 - P( Type II Error)

P( Type II error)

P( Accept H0 , when H0 is False)

This is two tailed test hence find two limits of sample mean value for which we accept null hypothesis H0 at 0.05 level of significance.

z values for 0.05 level of significance for two tailed test are:

Find Area = 0.05/2 = 0.025 and look in z table for 0.0250 and find z value.

z = -1.96

Since this is two tailed test , we have two z values. -1.96 and 1.96

Thus find sample mean and

that is:

and thus

Thus we accept H0 when sample mean is in between and .

Now find Probability of sample mean is in between and . when µ = 12

which gives Probability of type II Error.

P( Type II error)

Look in z table for z = -0.9 and 0.00 as well as for z = -4.8 and 0.02 and find area.

P( Z < -0.90) = 0.1841

As P( Z < -3.49) = 0.0002 , then P( Z <-4.82 ) = 0.0000

Thus

Thus Power of the test is: