Question

You wish to test the following claim at a significance level of 0.002

      H0:μ=66.5
      H1:μ≠66.5

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size 77 with a mean of 71 and a standard deviation of 9.9

What is the critical value for this test? (Report answer accurate to 3 decimal places.)
What is the test statistic for this sample? (Report answer accurate to 3 decimal places.)

Answer 1

Solution:

We do not know the standard deviation. So we use t test.

here n = 77

So, d.f. = n - 1 = 76

= 0.002

/2 = 0.001

Now, sign in H1 indicates that the two tailed test.

So, the critical values are   i.e.  

  =   _0.001,76 = 3.201  (using t table)

Critical values are 3.201

The test statistics t is given by ..

t =  

= (71 - 66.5)/(9.9/77)

= 3.989

The test statistics t = 3.989