Problem

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. An entomologist writes an article in a scientific journal which claims that fewer than 19 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. There is sufficient evidence to support the claim that the true proportion is greater than 19 in ten thousand. There is sufficient evidence to support the claim that the true proportion is less than 19 in ten thousand. There is not sufficient evidence to support the claim that the true proportion is less than 19 in ten thousand. There is not sufficient evidence to support the claim that the true proportion is greater than 19 in ten thousand.

Solution

Step 1 :The original claim is that fewer than 19 in ten thousand male fireflies are unable to produce light due to a genetic mutation.

Step 2 :The conclusion of the hypothesis test is to reject the null hypothesis. In hypothesis testing, the null hypothesis is usually a statement of no effect or no difference.

Step 3 :If we reject the null hypothesis, it means that we have found evidence that suggests the null hypothesis is not true.

Step 4 :In this case, rejecting the null hypothesis would mean that there is evidence to suggest that the true proportion of male fireflies unable to produce light due to a genetic mutation is not less than 19 in ten thousand.

Step 5 :Therefore, the conclusion in nontechnical terms would be that there is sufficient evidence to support the claim that the true proportion is greater than 19 in ten thousand.

Step 6 :Final Answer: \(\boxed{\text{There is sufficient evidence to support the claim that the true proportion is greater than 19 in ten thousand.}}\)

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