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I'm struggling with an interpretation of p-value and confidence interval. They are both in agreement, but yet, can't be used together to make one statement about population proportion. So...am I forced to emphasize one over the other in an inference of population proportion? And which should I pick?!?

  • Ho = p ≥ 90%
  • Ha = p < 90%
  • p-hat = 584/649 = 89.98%
  • p-value = 0.514 > .01; fail to reject null hypothesis
  • Confidence interval: 99% upper bound = 93%
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  • $\begingroup$ This seems very different to the question you were asking in comments. Which you pick (or whether you do something else) depends on the kind of inference you want to make. $\endgroup$
    – Glen_b
    Commented Apr 24, 2016 at 7:29

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The p-value answers the question "What is the probability of observing a result as extreme as the result I have, purely by chance, if I assume that the result should be zero on average?" The confidence interval answers the question "what is the interval around the mean that captures a given proportion of observations?" I'm not sure how to interpret your notation. What does p-hat represent? Is this the result of the test statistic? If so, I would go with something other than p, to avoid the possibility of confusing it with the p-value. Also, what is the confidence interval lower bound? zero?

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  • $\begingroup$ for the interpretation of a confidence interval: see section 3 of stats.stackexchange.com/questions/167972/… $\endgroup$
    – user83346
    Commented Apr 24, 2016 at 7:48
  • $\begingroup$ Travis, p-hat is the sample proportion. I used z-test statistic to calculate p-value. I'm not sure what the CI lower bound is... $\endgroup$
    – Harper
    Commented Apr 25, 2016 at 3:23

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