# Math Help - Hypothesis testing help !

1. ## Hypothesis testing help !

When testing gas pumps in michigan for accuracy enforcement officials tested pumps and found 1299 of them were not pumping accurately and 5686 were accurate. It was off by 3.3oz, for every 5 gallons pumped. Use a .05 level of significance to test the claim that less than 10% of Michigan pumps are inaccurate.

I understand that this is a hypothesis testing problem.

2. Originally Posted by msierra0290
When testing gas pumps in michigan for accuracy enforcement officials tested pumps and found 1299 of them were not pumping accurately and 5686 were accurate. It was off by 3.3oz, for every 5 gallons pumped. Use a .05 level of significance to test the claim that less than 10% of Michigan pumps are inaccurate.

I understand that this is a hypothesis testing problem.
We test $H_0=.1" alt="H_0=.1" /> versus $H_a>.1" alt="H_a>.1" />.

Now, if $H_0$ is true, then we use the unbiased estimator $\hat p = Y/n\approx .1860$ for $p$, with standard error $\sigma_{\hat p}=\sqrt{pq/n}\approx .003590$. So our test statistic is

$z=\frac{\hat p-p}{\sigma_{\hat p}}\approx 23.96$.

Clearly this is way off the radar for any reasonable level, and so we reject $H_0$ in favor of $H_a$.

3. thank you so much!