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2.7 Suppose that esting Ilo Uq versus Ilo for the following observed values of the tesi statistic 2,331 3.60 to = [.95 2.19wnere the Ivo sample sizes are n110. Both...

Question

2.7 Suppose that esting Ilo Uq versus Ilo for the following observed values of the tesi statistic 2,331 3.60 to = [.95 2.19wnere the Ivo sample sizes are n110. Both sample variances are Unknown but assumed equal Fina bounds on ine P-value

2.7 Suppose that esting Ilo Uq versus Ilo for the following observed values of the tesi statistic 2,331 3.60 to = [.95 2.19 wnere the Ivo sample sizes are n1 10. Both sample variances are Unknown but assumed equal Fina bounds on ine P-value



Answers

For Exercises 3 through $8,$ the null hypothesis was rejected. Use the Scheffé test when sample sizes are unequal or the Tukey test when sample sizes are equal, to test the differences between the pairs of means. Assume all variables are normally distributed, samples are independent, and the population variances are equal. Exercise 20 in Section $12-1$

What's upstart cots In this video, we are given an example, and we are asked to perform either a chef or a two key test. So this is the example where provided. So considering we have a neat, uneven sample, sizes were gonna want to perform a chef test. So this is the formula to calculate our test statistic. So let's go ahead to the Excel spreadsheet where I have the raw data and heard. So I have entered the data and performed an Innova because through the example, were given, we are told that, um, the differences are there's already a significant difference. So I just wanna had ended theano of a test. So I think the first thing we should do is calculate our critical value. So our critical value is found by taking the critical value from our F test and multiplying it by the degrees of freedom between groups. So that is our critical value. And now we're going to calculate the test statistic. So what we're gonna do is I'm gonna go ahead and pair these categories up, so cars I'm just gonna use one SUV will be too, and trucks will be three. So I'm gonna pair cars and SUVs, SUVs and trucks and then trucks and cars. And the first thing I'm gonna do to calculate the test statistic is I'm gonna do the differences in means squared. So I'm gonna do equals parentheses. And I'm going to go to the mean of cars cause that's one and subtract the mean of SUV's gonna close the parentheses, and I mean square. So I'm going to do the same thing for the rest of these. All right, So that's the differences in our means squared. If we go back to our formula now, we have to do the variance within and multiply it by one divided by our sample sizes. Okay, so let's go back to our excel spread she So I'm gonna do okay first. Going to calculate that one over n nonsense. So let's do over here. It's too. He fools one over and then and will be the sample size for car. So 1/5 waas one over the sample size for SUVs. Well, I have us over a lot going on. Okay, So let me just type for than against, Okay, so I'm gonna do that for the rest of them. So one over. Sample size for SUV plus one over sample size for Chuck's man. Last one. Okay, that's just gonna make it easier for us when we do our numerator divided by our denominator. Okay, so next thing we're gonna do is we're gonna take our means square with n group, and we're gonna multiply it by that value we just calculated. And then now we can calculate our f our test statistic really easily. So we just take our numerator divided by our denominator, and I can just pull out formula down or not. Okay, so we've calculated our critical values and our test statistics, so let's go back to our whiteboard and fill them in. So are critical value. Waas e 0.52 on. Yeah, Okay. Just making sure 8.52 and our test statistic for cars and SUVs. Waas 2.1. And for SUVs and trucks, it was 17.64 And for cars and trucks, it was 27.9 to Okay, So in order to know which of these is significant, we want to ask which of these is larger than our critical value. So it was 2.1 greater than 8.52 No. Is 17 greater than a yes? And is 27 greater than a yes? So these so SUVs and trucks. So the differences between those means or different and the difference between the means of cars and trucks are different. So to summarize this, we're gonna say there is sufficient evidence to conclude a difference. And I mean cost the drive. These this between hybrid cars and trucks and between SUV's and checks. Alright, guys, that's it for this video. I hope you learned a lot else. You next time.

What's up? Stock cats? In this video, we are asked to perform either a chef or two key test, and those are post talk tests for a one way and over. So this is the example were given, and these are. These are the costs of what costs oven oven her watts of the oven. So because the sample sizes are uneven, we are going to perform a chef test. So this is the test statistic. This is the formula for the test statistic. This is our CV says are critical value. And we are told that the Alfa level for the one way Unova tests was performed at a 10.1 Alfa level. So let's go to the Excel she that I have our raw data on. So I've already performed the one way and Nova because that's how they have the example set up. So now we are going to pair up our oven watts because a chef test is a pair wise test. So we're gonna pair up 1000 watts and 900 watts, 900 watts and 100 watts and 100 watts and 1000 watts. So to calculate the numerator for our test statistic. We're gonna want to take the difference of the means squared. So let's go ahead and do that. So we're gonna take the mean for the 1000 watt of in. We're going to subtract the mean of the 900 watt of in, and we're going to square that value, and we're gonna do that for the rest of the pair. Wise pair wise pairs. No cheese. Hey, off to a rocky start. But we can recover. So the this is our numerator, So are enumerators done. And now we want to calculate our denominator. So the first thing I'm gonna do is I'm actually gonna calculate, um, this portion here and then because we already have our difference within groups. We already have our means squared within groups already calculated. So we need to calculate the other part, which I'm gonna do right here. So one over sample size of 1000 want plus one over sample size of 900 watt. All right, so now too calculate our denominator. We are going to take our means square within groups, and we're going Teoh, multiply it by the other value we just calculated I'm gonna go ahead and pulls. Actually, I can't pull it down. Okay? Finally, to calculate our test statistic, we're going to take our numerator over our denominator, and I can pull the this value, these values down. So for 1000 and 900 watt oven, we have two point 91 for a test statistic. And for the 908 100 we have eight point 40 And finally, for the 800 the 1000 we have 19 0.28 Okay, so last thing we have to do is calculate are critical value, because that's how we're going to decide which pairs air. Significant. So we're just going to take our critical value from the Unova test and multiply it by our degrees of freedom between groups. So are critical. Value is 5.21 Okay, so let's go ahead and go back to our white boards so you can copy these numbers down, make it easy for us. Teoh reject or failed to reject, so to decide whether we have a significant para not We're gonna take the critical. I'm sorry. We're going to take the test statistic of that pair, and if it is larger than our critical value. Then we can reject our no hypothesis. So that means the pair will be significant. So is 2.91 larger than 5.21 No. Is 8.40? Yes. Is 19.28? Yes. So we have to significant pairs at the 0.1 council level. So let's go and summarize our results. So there is fish in evidence. Uh, the 0.1 for love will to conclude there is a difference in me and cost between between 908 100 watt of ends and 801,000 walk ovens. All right, that's it for this video. I hope you guys learned a lot Chelsea next time.


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