I conduct an experiment to get an estimate of a parameter, $p$. My estimate is $\hat{p}=6$. Suppose I choose $\alpha=.05$ and conduct the following test: $H_{o}: \hat{p}=4 ; H_{1}: \hat{p} \neq 4$. I fail to reject $H_{o}$. What can I conclude?
A) The probability of observing a 6 , when $p=4$, is greater than .05 .
B) The probability of observing 6 or less, when $p=4$, is greater than .05 .
C) The true value of the parameter is $p=6$.
D) The probability of observing 6 or more, when $p=4$, is less than .05 .

Question

Quizplus · Accepted Answer

Failing to reject $H_{o}$ means that the probability of observing a result as extreme as $\hat{p}=6$ under the assumption that $p=4$ is not sufficiently low (i.e., not less than the significance level of .05). This does not provide information about the probability of observing 6 or less, the true value of $p$, or the probability of observing 6 or more being less than .05.

I Conduct an Experiment to Get an Estimate of a Parameter