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10) Is achieving a basic skill level related to the location of the school? The results ofa random sample of students by the location of school and the number of st...

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10) Is achieving a basic skill level related to the location of the school? The results ofa random sample of students by the location of school and the number of students achieving basic skill level in three subjects is shown in the contingency table. At a = 0.05, answer the following: SubjectLocation Urban SuburbanReading 40 60Math 49 66Science 41 68[The two categorical variables here are Subject and Location with two and three Categories respectively] [Use Algebra first then Tech next]State th

10) Is achieving a basic skill level related to the location of the school? The results ofa random sample of students by the location of school and the number of students achieving basic skill level in three subjects is shown in the contingency table. At a = 0.05, answer the following: Subject Location Urban Suburban Reading 40 60 Math 49 66 Science 41 68 [The two categorical variables here are Subject and Location with two and three Categories respectively] [Use Algebra first then Tech next] State the null and alternate hypotheses (write it mathematically) andwrite your claim. (2 points) Find the standardized test statistic 3 Points) Decide whether to reject or fail to reject the null: 2 Points) Make an interpretation of your decision inthe context: 2 Points) 10



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(a) identify the claim and state $H_{0}$ and $H_{a},(b)$ find the critical value(s) and identify the rejection region(s), (c) calculate d and $s_{d,}(d)$ find the standardized test statistic $t,(e)$ decide whether to reject or fail to reject the null hypothesis, and (f) interpret the decision in the context of the original claim. Assume the samples are random and dependent, and the populations are normally distributed. If convenient, use technology. The scoring averages (in points per game) of 10 professional basketball players for their rookie and sophomore seasons are shown in the table below. At $\alpha=0.10,$ is there enough evidence to support the claim that the scoring averages have changed? (TABLE CANNOT COPY)

We want to conduct an F test of equality of population variance for the claim that population variances for populations one and two are equal at alpha equals 20.1 significance. We also have listed at the top from the randomly drawn samples from the population sample variances and sample sizes are just marked in blue. So we proceeded the five steps listed below A. Through E. To properly conduct this F. Test first we identify the hypotheses and critical value the distribution. So the hypotheses are no H. Not that the population minister equal H. A. They are not equal. So our claim is our no h not. We have critical value for half alcohol alpha equals 0.5 Notice that we have out because this is a two tailed test and for degree of freedom of numerator nine and degree of food, freedom of knowledge of 12. From the left table 5.20 here are test at at his computer at equal S one S two squared equals 1.14 So we can conclude the test since F is less than fc, we're not in the critical region, and we do not reject H not. This means we have evidence to support the claim made by the initial hypothesis.

Yeah. We want to conduct an F test of the quality of population variance for the claim that population variances the population one and two are equal at alpha equals 20.1 significance. We also have here the sample variances and sample sizes for the two random samples johnson these populations. So we proceed through steps one through five or rather a three us below to conduct this test properly. First we see the hypotheses and identified the critical value our hypothesis or rather no hypothesis is that the population variances are equal alternatives that they are not equal. So I claim as our a chart we have a critical value of one half output equals 10.5 because this is a two tailed tests, degrees remember generated 11 degree freedom denominator 13 from an F table that gives us 2.635 Our test dot f is f equals one square to us to square or 1.282 Thus were able to conclude the test. Since test dot F is less than 2.635 the critical value, that means we're not in the rejection region, so we do not reject H not, which means we have evidence to support the claim of the null hypothesis.

So we're looking at D. Being the difference between the batting average after clinic minus the batting average before taking the clinic and the coach thinks that his clinic helps. So that's what our little D. Is standing for. So on part A. We would be assuming that the main difference is less than or equal to zero and alternately that is greater than zero or that it's equal to zero. And that there is no different. So that's going to depend on how your structure is is having to do things. So on part B we want to look at that picture and we want to see where that cut off point is. So we're having here at zero and we want the the significance level to be I believe. 5%. Let me quick peek back at the question 5%. And so we have uh 14 pieces of data. So we need to look up that T. Value that has 13 degrees of freedom and has 5% in the upper tail. And when I look up that value, I am finding that value is 1.771 So our rejection region Will end up being if our test statistic with 13° of freedom is greater than 1.771. So now let's find our d. And I put all that data in my calculator and I just subtracted them just in my in my head. So hopefully I did that well. And when I did I got that the mean difference was .001. With a standard deviation of those values being .016 096 And so now we want to find that test statistic and the test statistic with 13° of freedom is equal to the difference. We got minus the difference we're assuming which is zero and that standard deviation over the square root of our sample size. Make sure you don't use the degrees of freedom. And when I did that, I got the test statistic not to be very big. It's .23246. So this value really should be. Well, this value is way up here. Let me put it up here. There's where my test statistic is so on Part E. We fail to reject the null. And what does that mean? Part app. That means that the clinic really didn't have an effect as no uh, no increase on that batting average. It was just fun.

The following is a solution to number 23 and this is about rabies in in Fox. Uh Fox regions. And the first part is just to verify that the sample mean for region one was 4.75 and that standard deviations 2.82 And then the sample, I mean for the second region is 3.93 and the standard deviation is 2.43. And they say use a calculator. So I'm assuming it's going to be a some sort of scientific or graphing calculator. So I went ahead and pre populated. If you go to status is a c. and if you go to stat edit, I went ahead and punched in those numbers already into L one, L two and then you can find these values fairly quickly. If you just go to stat and then one of our stats and then do your L one. So this is the verification. So X bar is 4.75 which what it was and then s. is about 2.82 and then would verify on the second one if you go to stat couch and then it's one of our stats and then second L. Two And we calculate that and that's verified. So 3.93 and then two 43 for the standard deviations, that's verify that first part Um using some technology, so that's how you would use it in the IT4. And the second part of this we actually do a um hypothesis test without formally writing everything down. So this is a two sample T test since we don't know what the population standard deviation is, just the sample standard deviation. So we're gonna use a T. Test and the significance levels point oh five. And what we're gonna do since we already have the data there, let's go ahead and say stat and then test and it's the two sample T. Test and I'm gonna keep it on data here because I already have the data listed into L. One L. Two and then the everything else can say the same. But the alternative um it says that that the two regions are just different either way so we don't know which one is bigger which was smaller. So whenever that's the case you're just gonna leave it as not equal to. And generally we're going to keep keep it as no on pooled unless it tells you otherwise. And then we calculate and that's gonna give us what we need. So the T. Value is 0.865 But really all I care about is this p value 0.394 So the p value so m. One is not equal to end to. That's the the alternative I guess and then the Noles that they're the same. But the p value is the important things of the P value equals point 394 And what we do is we explicitly compare the P value with the alpha value and in this case the p value is greater than alpha. So that means we fail to reject h not meaning we're not rejecting, meaning that these two means are the same. So if we put it and um you know, normal words, writing what we can say, I'm gonna type this because it'll be faster. There is not sufficient evidence to suggest that the mean number of cases of fox rabies is different In the two regions. So it's basically just saying that um these the mean number of rabies in these two regions are the mean number is approximately the same.


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