A pain clinic in Raleigh, North Carolina, treats 125 patients annually for pain.

Question

A pain clinic in Raleigh, North Carolina, treats 125 patients annually for pain. Of those, 48 present with fibromyalgia. The national average presenting with fibromyalgia in pain clinics is 60%. The investigaors wish to know whether they have significantly fewer proportions of fibromyalgia patients than the national average?

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

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.6 [NULL HYPOTHESIS]
Ha:   p   <   0.6 [RESEARCH HYPOTHESIS]

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Here, we use a z test for proportions. [ANSWER, Z TEST]

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If we set alpha = 0.05, as this is left tailed,

zcrit = -1.645 [ANSWER]

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As we see, the hypothesized po =   0.6      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.384      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.043817805      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -4.929503018   [ANSWER, TEST STATISTIC]

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As z < -1.645, we reject Ho.

There is significant evidence that the clinic has significantly fewer proportions of fibromyalgia patients than the national average at 0.05 level. The point estimate of the difference from 60% is round 21.6% lower than the national proportion.

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