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(10 points) one-factor ANOVA analysis produced P-value 0.035 . The tradli- tional values of the significance level are 0.01,0.05, 0.1_ (a) What is the smallest tr...

Question

(10 points) one-factor ANOVA analysis produced P-value 0.035 . The tradli- tional values of the significance level are 0.01,0.05, 0.1_ (a) What is the smallest traditional valuc of for which this result (P-value) significant? What is the largest tradlitional vale of ( for which this result (P_ value) is not significant' Suppose X; = 4,4 = 6 and X3 = 3.8, and the Tukey-Kramer critical value for 0 0.05 is CVTK 1.5. Which means are significantly different at the 0.05 level?

(10 points) one-factor ANOVA analysis produced P-value 0.035 . The tradli- tional values of the significance level are 0.01,0.05, 0.1_ (a) What is the smallest traditional valuc of for which this result (P-value) significant? What is the largest tradlitional vale of ( for which this result (P_ value) is not significant' Suppose X; = 4,4 = 6 and X3 = 3.8, and the Tukey-Kramer critical value for 0 0.05 is CVTK 1.5. Which means are significantly different at the 0.05 level?



Answers

Find the P-value for the hypothesis test with the standardized test statistic $z .$ Decide whether to reject $H_{0}$ for the level of significance $\alpha .$ Two-tailed test $z=-1.68$ $\alpha=0.05$

Now. This time my zip statistic is minus 1.55 minus 1.55 This is my Zed statistic, my Z statistic and my Alfa level A 0.5 My Alfa is 0.5 So now what I want to do is I want to find the p value for my set statistic and I use a P value calculated for that. This is a one tailed test. Since this is left tail and I get my P value of 0.606 my P value is 0.606 And since my P values greater than my Alfa, I failed to reject minor hypothesis. I fail to reject my it's not This would be my answer.

E want to check if these first two results are significant or not at given Alfa levels. So my first you statistic is 1.92 and degree of freedom is 44. In order to calculate the P value for the first one with P values 0.3 which is less than Alfa hence, I can say that the first one is significant. The second one mighty statistic is 3.41 degree of freedom was 44. My advice 0.1 So this is three point for one degree. Freedom is 44 Alfa 0.1 What is my P value? My P value. My P value is much less than 0.1 If it is lesser than that, it is definitely less than this. Hence, we can say that both of these results are significant at these Alfa levels. The third one, the third one I have been given tee off 44 is equal to 1.81 Now what will be the P value reported in one tail test and to tail test? First of all, let's understand what is a p value p value Is the probability off an event or something even rarer than that offering? If it is a mental test, what is a P value for this? This is 1.81 somewhere. The P value is going to be this region. But if But if this is a two tailed tests, I am going to have 1.81 here. And there is also a minus 1.8 When here, minus 1.81 here. And this is going to be the twice off it. So p value becomes Christ. So let me just try toe find the P value P is equal to 44 1.81 at 0.5 0105 years ago. The physical 40 40 years ago to 1.81 He is equal to 1.81 The last one I think I put I had in the second one, I had mistakenly put their 13.41 But you will find that even if I put 3.41 my people, it will be much less than that one. Much less than 0101 Okay, so 1.81 degree a few dollars. 44. And let's try a one tailed test. First one tail does to 0.38 Fight. If this were one tail test only this region is 0.3 Eat, face something. But now if this is a two tailed tests, it will get doubled because I want the area off both the sides. So there's going to be 0.7 something. Let's see. This is a two tailed test. This becomes 0.77 This becomes there's a brutal test. This become 0.77 So, yeah, P values less than 0.3. Value is less than 0.1 in both the cases. But if it were a one tailed test, P value would have been this. And if it were to tell test, the value would have been this

We have a hypothesis test with P values 0.083 for are observed data. We want to determine for each of the alphas or the significance values below whether or not our P value enables us to reject the null hypothesis each not before getting started. Let's remember a critical definition. You can reject the null hypothesis, H not whenever P is less than or equal to alpha. So whenever your P value is less than or equal to your significance level. Now implementing this in part A We have that 0.083 is greater than alpha equals 0.05. That means that P is greater than alpha. So for part a we do not reject the null hypothesis. For part B, alpha equals 0.1, 0.083 is less than or equal to 0.1. So in this case P is less than or equal to alpha. And we were able to reject the null hypothesis. Finally, for part C 0.083 is actually greater than the alpha value here of 0.06. So again P is greater than a, and once again we do not reject the null hypothesis.


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