Z-TESTS We will use the formula for Z from lecture notes, page 2. since H 0 is u

Question

Z-TESTS

We will use the formula for Z from lecture notes, page 2.

since H0 is usually m1=m2, then m1-m2= 0 and:

for 1, 2 known

for 1, 2 unknown

Z =                if n1 + n2 32

Steps to be covered:

State the hypotheses, and identify the claim

Find the critical value(s) – you might want to draw the curve

Compute the test (statistic) value

Make the decision to reject or not reject the null hypothesis.

PROBLEM 5:

Is there a difference between male managers and female managers when it comes to attendance? Test at .05 significance level

Female Managers: Average number of times absent from work = 10.9 days;

standard deviation = 2.4 days;    n = 10

Male Managers: Average number of times absent from work = 9.9 days;  

standard deviation = 1.8 days;    n = 20

Explanation / Answer

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0   [claim]

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At level of significance =    0.05          

As we can see, this is a    two   tailed test.  

n1 = sample size of group 1 =    10          
n2 = sample size of group 2 =    20          

Thus, df = n1 + n2 - 2 =    28          

Now, the critical value for t is              
              
tcrit = -2.048, 2.048 [ANSWER]      

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Calculating the means of each group,              
              
X1 =    10.9          
X2 =    9.9          
              
Calculating the standard deviations of each group,              
              
s1 =    2.4          
s2 =    1.8          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    10          
n2 = sample size of group 2 =    20          
Also, sD =    0.859069264          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    1.164050493   [ANSWER, TEST STATISTIC]

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where uD = hypothesized difference =    0          
As |t| < 2.048, WE FAIL TO REJECT THE NULL HYPOTHESIS.          

Hence, there is no significant evidence that there is a difference between male managers and female managers when it comes to attendance at 0.05 level. [CONCLUSION]

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