Two whooping cough (pertussis) outbreaks were detected by the CDC in 2011. In Po

Question

Two whooping cough (pertussis) outbreaks were detected by the CDC in 2011. In Portland, OR, there were 18 cases of whooping cough among the 80 children who were not vaccinated in the city. In Atlanta, GA, there were 6 cases of whooping cough among the 70 children who were not vaccinated in the city. The researchers at the CDC wish to know if there is a significant difference in proportion of whooping cough cases between Portland and Atlanta?

What is the null hypothesis?
What is the research hypothesis?

What is the appropriate test statistic? Z test t test f test (anova) chi-Square Goodness of Fit chi-Square Test of Independenc

What is the critical value for the test statistic? Just give the number, not the name of the test. E.g. for Z-test, upper-tail, just write:

What is the test statistic for this study? Just give the number, not the name of the test. E.g. for Z-test, upper-tail, just write:

Interpret your findings. Remember to include magnitude, direction, significance, outcome measure, and groups being compared for full credit.

Explanation / Answer

A)

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

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b)

Ha: p1 - p2   =/=   0   [ANSWER, RESEARCH HYPOTHESIS]

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c)

As we test proportions, we use Z TEST. [ANSWER]

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d)

For 0.05 level two tailed test,

zcrit = -1.96 and 1.96 [ANSWER]

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e)

Here, we see that pdo =    0   , the hypothesized population proportion difference.  

          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.225      
p2 = x2/n2 =    0.085714286      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.057438846      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    2.424939288   [ANSWER, TEST STATISTIC]

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f)
          
As z > 1.96, then we    REJECT THE NULL HYPOTHESIS.      
There is significant evidence that the true proportion of cases of whooping cough in Portland is significantly different (greater) than the proportion of cases in Atlanta at 0.05 level. The point estimate of the difference is around 13.93% greater for Portland.

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