Question

A sociologist claims that 25% of adults would describe themselves as organized. a random sample of 100 adults reveals 42 who describe themselves as organized. do these data provide convincing evidence that greater than 25% of adults would describe themselves as organized? use α = 0.01. the p-value of this test is 0.0526. what conclusion should be made? because the p-value of 0.0526 ✔ is greater than α = 0.01, we ✔ fail to reject h0. we ✔ have convincing evidence that 25% of adults would describe themselves as organized.

Answer 1

In this hypothesis test, we examine whether the data provides convincing evidence that more than 25% of adults would describe themselves as organized. Using the given p-value and significance level, we conclude that we do not have convincing evidence to support the claim.

Step-by-step explanation:

In this question, we are testing whether the data provides convincing evidence that greater than 25% of adults would describe themselves as organized. We are given that a sociologist claims that 25% of adults would describe themselves as organized. A random sample of 100 adults reveals that 42 of them describe themselves as organized.

To test this claim, we can use a hypothesis test. The null hypothesis, denoted as H0, is that the true proportion of adults who would describe themselves as organized is equal to 25%. The alternative hypothesis, denoted as Ha, is that the true proportion is greater than 25%. Since we are testing if the proportion is greater, this is a one-tailed test.

Using the given p-value of 0.0526 and a significance level of 0.01, we compare the p-value to the significance level. Since the p-value (0.0526) is greater than the significance level (0.01), we fail to reject the null hypothesis. This means that we do not have convincing evidence that greater than 25% of adults would describe themselves as organized.