Performing a Sign Test In Exercises 7–22, (a) identify the cla...

Question

Performing a Sign Test In Exercises 7–22, (a) identify the claim and state Ho and Ha, (b) find the critical value, (c) find the test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

Social Networking A research group claims that the median age of the users of a social networking website is less than 32 years old. In a random sample of 20 users, 5 are less than 32 years old, 13 are more than 32 years old, and 2 are 32 years old. At , can you support the research group’s claim? (Adapted from Pew Research Center)

Accepted Answer

All right, hello, everyone. So, this question says, a clinic director claims that the median patient wait time in the emergency room is more than 45 minutes. In a random sample of 18 patients, the recorded wait times relative to 45 minutes are as follows. Part one says to identify the claim and state Hno and H A. Part two says, at the 0.05 significance level, can you reject the director's claim? Interpret the decision. And here we have 4 different answer choices labeled A through D. All right, so first, let's begin by identifying our claim for part one. So our claim was stated in the text of the question. So the claim is that the population median wait time in the emergency room, or tau, is greater than 45 minutes. This would then correspond to the alternative hypothesis. So the null hypothesis, H not would state that ttau is instead equal to 45. And now we can test this at alpha equals 0.05. So first, what I'm going to do here is make the dataset visible on the screen again. Because the first step is to remove any ties. You want to remove observations that are equal to 45, and in this case, there are 2 of them. So, adjusting the sample size, N is equal to the original 18, subtracted by the two removed observations, to give you 16. And now you want to count the signs. So let's allow S positive to be the number of times that are greater than 45, and in this case, there are 12 of them. As negative then is the number of signs that are. Less than 45, which equals 4. So now, let's talk about the critical values. For a right-tailed sign test with N equals 16 and at alpha equals 0.05. Ultimately H not or the null hypothesis. Can be rejected. If S positive is greater than or equal to 12. Recall that in this case as positive was in fact equal to 12, which is greater than or equal to our critical value. So therefore, we can reject the null hypothesis. And so rejecting the null hypothesis means that at the 5% level of significance, there is enough evidence to support the director's claim that the median ER wait time exceeds 45 minutes. So here if I scroll up once more. Our correct answer is option A in the multiple choice. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.

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