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,

[APPLET] SAT Scores A guidance counselor claims that students who take the SAT twice will improve their scores the second time that they take the SAT. The table shows both math SAT scores for 12 students who took the SAT twice. At 0.01, can you support the guidance counselor’s claim?

Credit Card Charges A financial service accountant claims that the median credit card balance of college students is more than $500. You randomly select the credit card accounts of 12 college students and record the balance for each account. The balances (in dollars) are listed below. At , can you support the accountant’s claim? (Adapted from Sallie Mae)

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Accepted Answer

All right, hello, everyone. So this question says, a training coordinator claims the median weekly hours employees spend on professional development is less than 5 hours. You record the weekly hours for 12 employees listed as follows. Part one says to identify the claim and state H not and HA. And part two says, at the 0.05 significance level, can you reject the coordinator's claim? Interpret the decision. And here we have 4 different answer choices labeled A through D. All right, so first, let's begin with part one here. Now, first, we can find the claim because it's already been stated in the text of the question, right? The claim is that the population median weekly hours or T Is less than 5 or less than 5 hours. So, because of this, the claim would therefore correspond to the null hypothesis, or excuse me, the alternative hypothesis. So H A. Would be that tau is less than 5. This means that the null hypothesis. Would state instead that tau is equal to 5. So now we can test at alpha equals 0.05, and that's for part two. All right, so first and foremost, I want to scroll up very quickly to consider the data set that we're given. Because the first thing that we need to do is remove any ties in the data set. So we have to remove in this case, data points that equal 5. In this case, there are 3 of them, so we're going to eliminate those 3. This gives us a new sample size. So, the effective sample size is equal to the original 12, subtracted by the 3 that were removed, to give you 9. And now What you want to do is find the number of observations that are either less than 5 or greater than 5. Let's say that S. Negative is the number of observations that are less than 5, and in this case there are 5 of those. Now let's allow S positive to be the number of observations that are greater than 5. And that happens to be equal to 4. So here We're now left to find our critical values. Or a left tailed sign test with N equals 9. And at alpha equals 0.05, H knot. Is rejected If S negative is greater than or equal to 1. And in this case, recall that S negative here is equal to 5, which is in fact greater than 1. Or actually quick correction because I wrote down the wrong sign. For a left-tailed sign test with N equals 9 at alpha equals 0.05, H knot is rejected if S negative is less than or equal to 1. Heres negative is equal to 5, which is in fact Greater than one. And so because of this, we failed to reject. It not So what does that mean in context? Well, failing to reject H knot in this case means that at the 5% level of significance, there is not enough evidence to support the claim that the median weekly professional development hours is less than 5. This means that I scroll up here. Our correct answer is option D in the multiple choice. So for part one, H knot is tau equals 5, and HA is tau is less than 5. For part two, failed to reject HO. At the 5% significance level, there is insufficient evidence to support the claim that the median weekly professional development hours is less than 5%. And there you have it. So with that being said, thank you so very much for watching and I hope you found this helpful.

Key Concepts

Sign Test

Null and Alternative Hypotheses (Ho and Ha)

Critical Value and Decision Rule

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