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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.

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1 Answer 1

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In the second proposal above, you wrote:

In this case, the data would support the producer's claim if I do not reject the null hypothesis.

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.

Both your above proposals are technically valid hypothesis tests. However, if you are attempting to see if there is evidence to support the producer's claim, you will need to formulate that claim in the alternate hypothesis.

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