Exam 22: What Is a Test of Significance

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 are the null and alternative hypotheses in this situation?

If the value of the standardized test statistic is 2.5,

We would like to test the hypothesis that p = 0.5 versus the alternative that p < 0.5 using data from a random sample. We calculate the standard score to be -1.8. The P-value would then be

If a significance test gives P-value 0.005,

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 scientist is studying the relationship between the depth of a watermelon vines' roots and the weight of the watermelons produced. The scientist collects measurements from a random sample of vines. He then conducts a significance test in which the null hypothesis is that there is no correlation between the two variables (correlation = 0) versus the alternative that the correlation is greater than 0. From this test he found a P-value of 0.0032. What does this tell us?

We would like to test the hypothesis that  = 20 versus the alternative that   20 using data from a random sample. We calculate the standardized test statistic to be 1.2. The P-value would then be

A genetic theory says that a cross between two pink flowering plants will produce red flowering plants a proportion p = 0.25 of the time. To test the theory, 100 crosses are made and 31 of them produce a red flowering plant. Is this evidence that the theory is wrong? What are the null and alternative hypotheses in this situation?

Among the findings of the American Religion Identification Survey (ARIS) of 1,710 college students in 2013 was their response to whether religion is the root cause of conflicts around the globe. Asked whether religion brings more conflict than peace, 47 percent said Yes, 41 percent said No, and 12 percent were unsure. The P-value for the test in the previous question is about 0.99. This means that:

A city ordinance requires that more than 75% of its residents must agree to the construction of new public buildings (using tax dollars) before any such structures can be built. A proposal has been made to build a new recreational facility in the city, and sponsors of the proposal want to conduct a small survey to see if it would be approved if put to an official vote of all residents. A simple random sample of 150 residents revealed that 123 supported a change (and 27 did not). What are the null and alternative hypotheses in this situation?