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 = <u><em>population proportion of students wanting to reduce gluten at the university.</em></u>
So, Null Hypothesis,
: p = 30% {means that the proportion wanting to reduce gluten at the university is the same as for all adults}
Alternate Hypothesis,
: 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 <u>One-sample z test for proportions;</u>
T.S. =
~ N(0,1)
where,
= sample proportion of students who would say they want to reduce or be free of gluten =
= 0.20
n = sample of students taken = 25
So, <u><em>the test statistics</em></u> = ![\frac{0.20-0.30}{\sqrt\frac{0.20(1-0.20)}{25} {} }](https://tex.z-dn.net/?f=%5Cfrac%7B0.20-0.30%7D%7B%5Csqrt%5Cfrac%7B0.20%281-0.20%29%7D%7B25%7D%20%7B%7D%20%7D)
= -1.25
The value of standardized z test statistic is -1.25.