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 50 students at her university and 13 (or 26%) of them say they want to reduce or be free of 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 (i.e. the same as the general population) versus the alternative hypothesis that a smaller proportion of students would say they want to reduce or be free of gluten.

What is the value of the test statistic for this hypothesis test?

	The test statistic is less than -1.0.
	The test statistic is between -1.0 and -0.75.
	The test statistic is between -0.75 and -0.50.
	The test statistic is between -0.5 and -0.25.
	The test statistic is between -0.25 and 0.

Answer 1

Here claim is that a smaller proportion of students would say they want to reduce or be free of gluten.

So hypothesis here is vs

And

Hence test statistics is

So answer here is

The test statistic is between -0.75 and -0.50.