# Identifying the alternate hypothesis [basic]

I was dealing with the following question:

After a change management, a producer claimed that less than 5% of his flak jackets have production flaws. A sample of 200 flak jackets was randomly collected for which 5 exhibited production faws. Does the data that supports what the producer claimed? (Use $$\alpha=0,05$$).

I'm struggling to identify the correct alternate hypothesis for the test. As he claimed "less than 5%", then I infer that I should test: \begin{align} H_0&:p\geq0,05 (\text{ no less than 5% of flak jackets have production flaws})\\ H_1&:p<0,05 (\text{less than 5% of flak jackets have production flaws}) \end{align} The data would support the producer's claim if I reject the null hypothesis. At the same time, I think that the following test is also acceptable: \begin{align} H_0&:p\leq0,05 (\text{ no more than 5% of flak jackets have production flaws})\\ H_1&:p>0,05 (\text{more than 5% of flak jackets have production flaws}) \end{align} In this case, the data would support the producer's claim if I do not reject the null hypothesis.

Which one is correct?

I appreciate any feedback.

This is incorrect. This is because a failure to reject $$H_0$$ does not mean that there is evidence to support $$H_0$$. All you are allowed to say is that the evidence does not significantly support $$H_1$$ at the nominated $$\alpha$$ level; you cannot say anything about whether $$H_0$$ is likely.