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The scores of 36 trainees assigned to three trainers and three training programs on a 50-point job [ performance test administered at Ihe end of the training period...

Question

The scores of 36 trainees assigned to three trainers and three training programs on a 50-point job [ performance test administered at Ihe end of the training period are in Ihe table below_ State and test the appropriate hypolheses at the 0.01 level of significance_ SSCORES OESA TRANNEES Becter ATRANERSLEVELquartethAetor PROORAMSLEYEL ?:BanacnnLEVEL3 1se 023 40gcubcaranunL41

The scores of 36 trainees assigned to three trainers and three training programs on a 50-point job [ performance test administered at Ihe end of the training period are in Ihe table below_ State and test the appropriate hypolheses at the 0.01 level of significance_ SSCORES OESA TRANNEES Becter ATRANERS LEVEL quarteth Aetor PROORAMS LEYEL ? : Banacnn LEVEL 3 1se 023 40g cubcaran unL 41



Answers

For Exercises 3 through $12,$ use the Wilcoxon rank sum test. Assume that the samples are independent. Also perform each of these steps. a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Job Satisfaction Two groups of employees were given a questionnaire to assess their degree of satisfaction with their jobs. The questionnaire scores range from 0 to $100 .$ The groups are divided according to years of service. The data are shown. At $\alpha=0.10,$ can you conclude that there is a difference in job satisfaction between the groups? (Table cannot copy)

So, you know, the formula for main squares for both treatment and error Is simply mean squares is equal to the sum of squares over 80° of freedom. And similarly, we know the formula for the EFTA statistic isn't the Mst over the MSC. It's now using these formulas, we can start and filling out the values for this table. So for the treatment the main squares is simply going to be 2,814 over three. Just 9 38. And for the air it will be 4915. Okay, Over 36. Just 1 36.53. So 1 36.5 and 9 30 eight. Not for the after statistic, simply going to be 9 38. Over 1 36.53. Yeah. Which will give us 6.87. Yeah, I'm pretty total. Can simply sum up the Values respectively 7th 7 and 29 and 39.

All right guys, so for this one, um First we need to start by identifying or null and alternative hypotheses are no hypothesis is that there is the same variants being male and female professors and alternative hypothesis that there's there's a difference between male and female professors when it comes to variation variants, I should say. Um So okay, so with that um with that, what the next thing we need to do is we need to go ahead and identify our f statistic. Um and that is going to be found by opening a google sheet, at least in my case I opened google sheet and I want to hand his input all the data from the table. Okay. In order to find our F test statistic first and put in the day to the next thing I did as I found the variance. Okay, it's by the V A R equals V A R in a cell and I highlighted the data. I wanted to find the variance in and I enter and then the variance for the second one was right there. I hit enter. Awesome. Okay, cool. So it looks like the variance for the few professors is much higher. So it looks like our female professors. Well BS one sq and our male friends will be S two squared because s one square it has a higher variance. So to find the F. Test statistic, I just need to divide the larger variants by the smaller variance and there it is 4.175 Very large F statistic right there. All right. So the next thing I need to do is this I need to calculate the p value in order to calculate the P value with an F statistic. You do need to have the F statistic, but we also need to find degrees of freedom for the data. So here's what I'm gonna do that in google sheets. Of course I could count manually. But if another way to do it is actually just do this do equals count and it will actually count all this stuff for you. Okay. But degrees of freedom isn't a direct count, degrees, freedom is account minus one. And so that's what I'm going to put and that's gonna be nine and this should be the same. But let's just check just in case count of that minus one and there we go. Nine. Okay. So for my p value, what I'm gonna do is I'm going to start an F. Distribution also known as F. Dist and open parentheses and idea input. Three values the first value, the F statistic and the second two values are the degrees of freedom. Close my parentheses do that and we get a fairly small, we get a very small p value right there. However, what we do need to do is this we're not quite done yet because this is a one tailed P value. What does that mean? That means this P value of work. If that is a less than or greater than symbol, It's a non equal simple, not equal, simple is a two. Uh is a two way distribution. Okay? Which means it's going to be twice as large as a one way, which means in order to get the correct value, I need to take this and multiply or asterisk in google sheets by two. And that is my p value right there. So this p value, they asked us to use 0.5 significance level. Is that less than 0.5 barely. But yes, that is less than 0.5 So there is sufficient evidence to reject the null hypothesis. So there is sufficient evidence to reject the null hypothesis.


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