Performing a Runs Test In Exercises 15 – 20, (a) identify the ...

Question

Performing a Runs Test In Exercises 15 – 20, (a) identify the claim and state H0 and Ha. Use α = 0.05

Coin Toss A coach records the results of the coin toss at the beginning of each football game for a season. The results are shown, where H represents heads and T represents tails. The coach claimed the tosses were not random. Test the coach’s claim.

H T T T H T H H T T T T H T H H

[APPLET] Dog Identifications A team of veterinarians record, in order, the genders of every dog that is microchipped at their pet hospital in one month. The genders of recently microchipped dogs are shown, where F represents a female and M represents a male. A veterinarian claims that the microchips are random by gender. Do you have enough evidence to reject the doctor’s claim?

M M F M F F F F F M M M F F

F M F F F F F M F F F M F F F

Accepted Answer

Hi, everybody. Our next question says, a wildlife researcher records in order, the species of birds. S for sparrow, R for robin, that visit a feeder over 2 weeks. The sequence is as follows, and then we have the sequence of S's and R's, we'll go back to that. The question then continues. The researcher claims that the bird visits are random for species. At alpha equals 0.05, do you have sufficient evidence to reject the researcher's claim using a runs test? There is insufficient evidence to reject the claim that the bird visits are random by species. B, there is sufficient evidence of non-randomness. C, the test is inconclusive, or D, more data is needed. So let's think our way through the runs test for randomness. We'll start with our hypotheses as always. In this case, the null hypothesis is that the sequence is random. And then the alternative hypothesis. Is that the sequence is not random. So, let's look at the data that we have and see, do we have sufficient data to run that RES test. Well, what do we need to test that? We need to know our N1. N2, so the number of variable 1 and the number of variable 2. And we need to know the number of runs, which is labeled as capital G. Now, if these N1 and N2 values are greater, each greater than 20. Or excuse, excuse me, I should say, if either N1 or N2 is greater than 20, you can assume a normal distribution. Um, in this case, let's count, um, but just glancing over that seems unlikely, but that's all right, even if we can't assume a normal distribution, we have a table to look up critical values for runs test. If RN1. And N2 are both less than or equal to 20. So let's go ahead and look for a number of runs and then the number of each variable. So, to look for the number of runs, remember we're looking for a, we're looking for the same variable with, you know, together with either 0 or different variable on the other side. So, our sequence starts with SR. So, that S, that single S by itself is one run. And then after the R, we have two S's. So again, that single R, another run. Our two S's are followed by two R's, so the two S's are another, another run. The two Rs are followed by 3 S's. So the two R's, so now we're up to 1234. The 3 S's are followed by 3 Rs, so the three S's are another one. The 3 R's followed by 3 S's. So, another run for the 3 R's, 3 S's followed by an R. So, the 3 S's is another one. That is a single R followed by 3 S's. So, the single R makes a run. 3 S's are followed by a single R, so, the S's make a run. And then that R is a run by itself. After the R 3 S's, R and then SS. So, 3 S's are a run, the R is a run, and the last 2 S's are a run. So let's count how many runs we have here. We have 123456789, 1011, 1213. So RG or number of runs. Is equal to 13. And our N1. We'll say is I'm gonna put. R next to it, that will be the R. Or I guess it would make more sense to make it S since S is the first in the sequence. It doesn't matter because we're going to be looking at both of them. So, whichever you want to call N1 N2, either way is fine. And then we'll call R and 2. So, let's see how many S's we have. I will highlight them in blue to make them stand out from each other. So, for S's, we have one. 23456789, 1011, 1213, 1415. And 1617. So we have 17 as our N1. And then for ours, we have 123456789. So, N2 is 9. So, we have all the values we need, so we can cross that choice D, more data is needed. And since our N1 and N2 are both. Less than or equal to 2. A little check mark. So we're going to look at our critical values for runs table. And that's going to give us 2 values. So it'll give us a lower critical value and an upper critical value. So we use, and again, I'll highlight blue on our table, and 1 equals 17 and N2 equals 9. And we see that when we look at the table, the lower value is 7. And the upper value is 18. And so that means that we reject our null hypothesis, if our number of runs is less than or equal to 7, the lower number. Or if G is greater than or equal to 18. Which makes sense because we're looking for an extreme number of runs that would indicate this, this isn't a random pattern. So since our G is 13. That is not in that rejection region. 13 is between 3 and 8, 13 is between 7 and 18, so we'll say 7 is less than 13, which is less than 18, so we fail to reject the null hypothesis. So, that's going to give us the answer of choice A. There is insufficient evidence to reject the claim that bird visits are random by species. Choice B is incorrect, because that would be only if our G value was in the rejection region. And then, of course, choice test is inconclusive is incorrect because our test is conclusive. We could see clearly that we have this value of G that is in the. Expected range of the number of runs if the visits were random. So again, we have this sequence of bird visits to a feeder, and the researchers claiming that the bird visits are random. Add alpha equals 0.05, which is standard for these runs, the runs table. Do we have sufficient evidence to reject the researcher's claim using a runs test? So, we did our runs test, looking up the critical values for the runs table, and our number of runs was not lower than the lower critical value or higher than the upper critical value. So our answer is choice A. There is insufficient evidence to reject the claim that bird visits are random by species. See you in the next video.

Key Concepts

Hypothesis Testing

Critical Values

Runs Test

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