In a recent national poll, 30% of adults said they wanted to \"cut down or be fr

Question

In a recent national poll, 30% of adults said they wanted to "cut down or be free of gluten.” A researcher wonders if a smaller proportion of students at her university would respond in the same fashion. Suppose the researcher conducts a survey of a random sample of 25 students at her university and five of them say they want to at least reduce gluten. A statistician carries out a significance test of the null hypothesis that the proportion wanting to reduce gluten at the university is the same as for all adults versus the alternative hypothesis that a smaller proportion p of students would say they want to reduce or be free of gluten. What are the null and alternative hypotheses in this situation?

A. Ho: p = 0.30 Ha: p < 0.30
B. Ho: p = 0.30 Ha: p > 0.30
C. Ho: p = 0.20 Ha: p < 0.30
D. Ho: p = 0.20 Ha: p 0.30

Explanation / Answer

Here the null hypothetical value is the proportion of adults who said they wanted to "cut down or be free of gluten" i.e. 30% = 0.3.

In the test, we have to check whether the proportion of students wanting to reduce gluten at the university is less than 0.3. So, the alternative hypothesis is p < 0.30.

Hence, here Ho: p = 0.30 and Ha: p < 0.30.

Hence, Option (A) is the correct choice. (Ans).

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