Question

Questions 6 and 7 are wo provided. rth 2 points each. Provide the correct answer directly on this page in the space 6. You are conducting the following hypothesis test at a signift cance level of a 01: If n - 9 and n2 25, what is the lef-tailed crtical value for rejecting the null hy #6 ANSWER: You have just conducted a two-tailed hypothesis test of the difference between 2 independent population proportions. The value of the test statistic is determined to be: z =-1.27. Using ONLY the appropriate statistical table in your textbook, what is the p-value of the hypothesis test? 7. #7 ANSWER:

Answer 1

6) Given      
n₁ = 9      
n₂ = 25      
Let α = 0.01  1% level of significance    
Let σ₁ , σ₂ be the population standard deviations      
       
The null and alternative hypothesis are       
Ho : σ₁² ≥ σ₂²      
H1 : σ₁² < σ₂²      
       
We find the critical F-value from the F-tables for α = 0.01
For left tailed critical value, we find the critical value for       
F_{1-α, n1-1, n2-1}= F_{(1-0.01), 8, 24}      
We use Excel function F.INV.RT for finding this
F-crit = F.INV.RT(0.99, 8, 24) = 0.1894
#6 Answer : 0.1894
    
       
7) z = -1.27      
This is a two tailed hypothesis test      
Using z-tables we find the p-value for z = -1.27      
(Use the z-tables for negative z and find area to the left of the z and you get 0.102)      
or       
(use the z-tables for positive z and find area to the right of the |z|      
subtract this area to the right of the |z| from 1 and you get 0.102)      
p-value = 2 * P(Z < -1.27)      
                = 2 * 0.1020                    (Multiply by 2 since this is a two tailed test)    
                 = 0.204      
p-value = 0.204      
#7 ANSWER : 0.204