Question

Given the following hypotheses:

H₀: μ = 400

H₁: μ ≠ 400

A random sample of 12 observations is selected from a normal population. The sample mean was 407 and the sample standard deviation 6. Using the 0.01 significance level:

1. State the decision rule. (Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.)
2. Compute the value of the test statistic. (Round your answer to 3 decimal places.)
3. What is your decision regarding the null hypothesis?

Answer 1

a) Decision rule : Reject H0, if | t calculated | > 3.106................by using =TINV(0.01,11) or by using t table.

or reject H0 if t < -3.106 or t > 3.106

b)

We have for given sample,                  
Population mean for given sample=400  
Sample mean=407          
Sample standard deviation s=   6      
Sample size =n=12          
                  
Degree of freedom = n-1 =11      
                  

t test statistic formula is

c) 4.04 > 3.106

Therefore, we reject H0.