Critical value and test statistic

Question

You wish to test the following claim (HaHa) at a significance level of α=0.01α=0.01.

      Ho:μ=73.1

      Ha:μ≠73.1

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=104 with a mean of M=77.2 and a standard deviation of SD=19.9.

What is the critical value for this test? (Round to three decimal places.) 

Critical value = ±

What is the test statistic for this sample? (Round to three decimal places.) 

Test statistic = 

Answer 1

You will use the t-distribution for this test because you don't know the population standard deviation.

The degrees of freedom = 104-1 = 103.

For a two-sided test need to look at 0.01/2 = 0.005 tail value as the critical value which is 2.624.

So critical value = +/- 2.624.

t = (77.2 - 73.1)/(19.9/sqrt(104)) = 2.101.