# Conclusion from Hypothesis Testing and CI

Can you draw a conclusion from combining results of hypothesis testing and confidence interval? For example, here is a fictitious hypothesis test for 1-proportion:

• Ho = p ≥ 90%
• Ha = p < 90%
• p-hat = 584/649 = 89.98%
• p-value = 0.514 > .01; accept null hypothesis
• Confidence interval: 99% upper bound = 93%

Therefore, can one state that true population proportion is between 90 – 93%?

• No, this is not a valid approach. Hypothesis tests and CI's answer different questions. They should be consistent if both are of the same size (not always true depending on how you construct your CI).
– user75138
Apr 17, 2016 at 3:46

can one state that true population proportion is between 90 – 93%?

No.

In fact neither component works that way alone

• A confidence interval doesn't let you state that the true population proportion lies inside the interval. Confidence intervals allow you to make a probability statement, but it's not even about the probability that the true proportion lies in the interval.

• A failure to reject the null doesn't tell you that the null is actually true, it just tells you that the probability of observing a sample proportion at least that small given the true $p$ was at least $0.9$ isn't very small.

So there's really no reason to think that the two together would suddenly confer the ability to make the kind of claim the two kinds of analysis wouldn't give you on their own.

• I'm struggling with the interpretation of p-value and confidence interval. They are both in agreement, but yet, can't be used to make one statement about population proportion. So what can be said about the population proportion? Apr 24, 2016 at 4:15
• @Harper that's a new question, but one that to some extent already answered by existing questions about interpretation/definition of confidence intervals and similarly for hypothesis tests. If you can't locate what you need from our search bar I'd suggest asking a new question of very similar form to the on in your comment Apr 24, 2016 at 5:18