Question

A sample of 37 observations is selected from one population with a population standard deviation of 4.0. The sample mean is 100.5. A sample of 56 observations is selected from a second population with a population standard deviation of 4.4. The sample mean is 98.6. Conduct the following test of hypothesis using the 0.05 significance level.

H₀ : μ₁ = μ₂

H₁ : μ₁ ≠ μ₂

1. Is this a one-tailed or a two-tailed test?

• One-tailed test

• Two-tailed test

2. State the decision rule. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

3. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

4. What is your decision regarding H₀?

• Reject H₀

• Do not reject H₀

5. What is the p-value? (Round your answer to 4 decimal places.)

Answer 1

a) gtwo tailed test

b)

α=0.05

reject Ho, if z <-1.96 or z >1.96

c)

sample #1   ------->              
mean of sample 1,    x̅1=   100.5000          
population std dev of sample 1,   σ1 =    4          
size of sample 1,    n1=   37          
                  
sample #2   --------->              
mean of sample 2,    x̅2=   98.6000          
population std dev of sample 2,   σ2 =    4.4          
size of sample 2,    n2=   56          
                  
difference in sample means = x̅1 - x̅2 =    100.5   -   98.6   =   1.9
                  
std error , SE =    √(σ1²/n1+σ2²/n2) =    0.8821          
                  
Z-statistic = ((x̅1 - x̅2)-µd)/SE =    1.9   /   0.8821   =   2.15

d)

reject Ho

(because z stat > 1.96)

e) p-value =        0.0312   [excel formula =2*NORMSDIST(z)]