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> =
= -1.25
The value of standardized z test statistic is -1.25.