Question

Given Hypothesis: Ho: population mean μo = 200 Ha: population mean μo < 200 This is Left-Tailed test. Population Standard Deviation σ = 50. Given Significance Level is 0.10 (10%). Critical z-value for 0.10 significance level and Left-Tailed test is (-1.28). Rejection Region will be to the left of z= - 1.28. -3…………..-2………….-1…………0……….1 Choose your sample mean, x̅ (any integer between 180 and 195) and your sample size, n, ( any integer between 16 and 36). Perform the steps below and reach your conclusion: reject Ho or do not reject Ho. Steps to follow: 1. Calculate your test statistics z-value: z = ( x̅ - 200) / (50/√n) 2. Compare your z value with the critical value -1.28. 3. If your z-value is less than -1.28 (falls in Rejection Region) then reject Ho. If your z-value is greater than -1.28 (does not fall in Rejection Region) then do not reject Ho. Show all three steps; just the answer will not be graded.

Answer 1

Ho :   µ =   200
Ha :   µ <   200

α=0.10

critical z value, z* =       -1.28

Rejection Region will be to the left of z= - 1.28

      

population std dev ,    σ =    50.0000                  
let Sample Size ,   n =    20                  
let Sample Mean,    x̅ =   185
                          
'   '   '                  
                          
1) Z-test statistic= (x̅ - µ )/(s/√n) = (   185 -   200   ) / (50/√20) =   -1.342

2) z stat < -1.28

3) reject Ho because z-value is less than -1.28 (falls in Rejection Region)