Find the p-value given the following null and alternative hypothesis with a test statistics of 2.153.

Null: p=0.56
Alternative: p not equal 0.56

Question

Find the p-value given the following null and alternative hypothesis with a test statistics of 2.153.

Null: p=0.56
Alternative: p not equal 0.56

rvc · Answer

it is binomial distribution?

awy · Answer

i dont think so, this is it asked

awy · Answer

and given

anonymous · Answer

It looks like $p=0.56$ is a proportion as part of the null hypothesis. You want to find the estimated proportion $\hat{p}$ given that the test statistic $Z=2.153$.

The $Z$ statistic for proportions is given by
$$Z=\frac{\hat{p}-p}{\sigma_p}=\frac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$$
Plug in everything you know:
$$2.153=\frac{\hat{p}-0.56}{\sqrt{\dfrac{0.56(1-0.56)}{n}}}$$
Ideally, you would solve for $\hat{p}$, but without a sample size I'm afraid there's not much you can do in the way of finding an actual value for $\hat{p}$...

awy · Answer

Alright, thx for the reply. This was a exam question and quite a curve ball since the homework and group assignments never included how to find the p-value without a sample size.

anonymous · Answer

@awy It's possible that I misinterpreted what the question meant by "p-value." This could be the p-value you would obtain from the actual statistical test for significance.

However, I don't see how you'd be able to find that either, since you need the significance level of the test. You can probably assume a 5% significance level (that's the standard level) and determine the rejection region for the test.

In this case, if we assume a 5% significance level, then the rejection region is $|Z|>1.96$ (keep in mind this is a two-tailed test). Since $2.153>1.96$, you reject the null hypothesis. I'm getting that the p-value is 0.031319.