Question

In a recent poll, 30 percent of adults said they wanted to "cut down or be free of gluten," according to The NDP Group, the market-research company that conducted the poll. 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 is the value of the standardized test statistic for this significance test? A) – 0.100 B) – 1.250 C) 0.200 D) – 1.091

Answer 1

Answer:

The value of the standardized test statistic for this significance test is -1.25.

Step-by-step explanation:

We are given that in a recent poll, 30 percent of adults said they wanted to "cut down or be free of gluten".

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.

Let p = population proportion of students wanting to reduce gluten at the university.

So, Null Hypothesis, $H_0$ : p = 30%      {means that the proportion wanting to reduce gluten at the university is the same as for all adults}

Alternate Hypothesis, $H_A$ : p < 30%     {means that a smaller proportion of students would say they want to reduce or be free of gluten}

The test statistics that would be used here One-sample z test for proportions;

                           T.S. =  $\frac{\hat p-p}{\sqrt\frac{\hat p(1-\hat p)}{n} {} }$  ~ N(0,1)

where, $\hat p$ = sample proportion of students who would say they want to reduce or be free of gluten = $\frac{5}{25}$ = 0.20

            n = sample of students taken = 25

So, the test statistics  =  $\frac{0.20-0.30}{\sqrt\frac{0.20(1-0.20)}{25} {} }$

                                     =  -1.25

The value of standardized z test statistic is -1.25.