1 Identify H0 and Ha 2 Identify the level of significance 3

(1) Identify H0 and Ha. (2) Identify the level of significance . (3) Find the critical value(s) and identify the rejection region(s). (4) Find the standardized test statistic. (5) Decide whether to reject H0. (6) Interpret (Answer the question).

The survey shows the percentages of customers waiting 20 minutes or less at two district offices of the Department of Motor Vehicles (DMV) in Virginia: Fairfax North is 60% and Fairfax South is 51%. Assume the survey included 400 people from each district. At = 0.05, can you reject the claim that the proportion of customers who wait 20 minutes or less is the same at the Fairfax North offices and the Fairfax South offices?

Solution

1.

Let p1 = population proportion for north
p2 = population proportion for south

Formulating the hypotheses          
Ho: p1 - p2   =   0  
Ha: p1 - p2   =/=   0   [ANSWER]

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2.

alpha = 0.05, as given.

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3.

zcrit = +/- 1.959963985       [ANSWER]

Thus, reject Ho if z < -1.959963985 or z > 1.959963985. [ANSWER]

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4.

Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.6      
p2 = x2/n2 =    0.51      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.034996428      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    2.571691002   [ANSWER, TEST STATISTIC]
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5.  
          
As z > 1.96996, then we    REJECT THE NULL HYPOTHESIS.      

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6.

There is significant evidence that the the proportion of customers who wait 20 minutes or less is NOT the same at the Fairfax North offices and the Fairfax South offices. [CONCLSION]