Answer the following questions Do not be afraid to ook in the textlThe effect size of a study Eood indicator of its practical importance because; unlike statistical...

A high school teacher has designed a new course intended to help students prepare for the mathematics section of the SAT. A sample of $n=20$ students is recruited for the course and, at the end of the year. each student takes the SAT. The average score for this sample is $M=562 .$ For the general population, scores on the SAT are standardized to form a normal distribution with $\mu=500$ and $\sigma=100$. a. Can the teacher conclude that students who take the course score significantly higher than the general population? Use a one-tailed test with $\alpha=.01$ b. Compute Cohen's $d$ to estimate the size of the effect. c. Write a sentence demonstrating how the results of the hypothesis test and the measure of effect size would appear in a research report.

Problem. We're gonna test a pairs. Any significant difference between the population average movie scene and then the sample average movie scene Given that the sample size 40 m standard deviation is 3.2, at the significant level is Poile five. So let's state the hypothesis that know her father's there will be new it go to 8.5 and then the alternative hypothesis will be meal is not a four pipe. So this is to tell task problem. So for Alfa is Pie 05 and then the critical values there will be two of them. So at Alfa over to which is boy 0 25 So that gives the value ISS plus minus 1.96. And then when the test value it will be the equal to expire minus for you over Signal was squared up in which is 9.6 miles, 8.5 over 3.2 overseas where we're 40. So I got to play 17. So let's look at the distribution grab. So seeing this is to tell tests here, I'm gonna have our over to an opera over two on the right tail. So this gave the Z Valley off negative 1.96 this is a positive 1.96. And then the test value is two boys 17. So is in this region, so we can call that we're gonna reject. It's not, and the result will be. There's enough evidence that there's difference between the, um, population average and then the sample average that there is a difference between the population Irish. This is thes simple, lavish.

All right. We have a sample of size and equal 73 of the 73 objects in the sample, 56 meet a certain criteria. And you want to observe our equals 56. We want to use this data to test the claim that the population proportion P does not equal 560.82 at a confidence level of 1% or alpha equals 10.1 Now that we've identified the confidence level, we can proceed in the following steps to conduct this test first is the normal distribution appropriate to use? Yes, it is because both NP and qpr greater than five. What hypotheses are retesting? We're testing them. No P equals 0.8 to the alternative. P does not equal 0.82 meaning we're testing or rather conducting a two tailed tests for this population proportion. Next compute p hat in your test statistic Piatt is simply are over and equals 20.77 We plug that along with PQ and and into the Z stat formula on the right to obtain Z equals negative 1.18 next to the P value. The p value can be found using it a lot google and textbook. And is the area outside of our positive, negative Z scores. This is a two tailed test, A. K. A. The area to the left of negative 1.18 An area to the right of 1.18 as is highlighted on the graph on the right. This gives P equals 0.2380 Next we reject H not no, we do not because he is greater than alpha. And we interpret this finding suggests we lack evidence that P does not equal 0.82

We're going to test if there's enough evidence that the average expenditure off our student is changed for the significant level off Alfa equal to 0.1 So let's stay the hypothesis H not, is me. We go to 10,337 and each one his meal is not 10,337. So this is to tell test. So we're gonna have to critical value one positive and one native at Alfa over two, which is your boy? 005 That's give us the ego to plus and minus 2.58 and the test value is 10,798 minus 10,337. Over 1000 miners, 60 over the square root off 1 50 So this gave me three boys 62. So we have the two tail critical region at Apple. Over to that gives a Z value is 2.58 negative two point pretty and my test value is 3.62 which is here. So is in the critical region. So we are going to reject is not an except H one at the significant level Alfa equal to 0.1 So we conclude that there is enough evidence that the expenditure has changed at Alfa equal to 0.1

The following is a solution for number 37. And it's actually data we've used before, the S. A. T. Math scores. The mean is 514. And the standard deviation for the population 113. And there is a product, I guess that says that they can raise the math scores so they sampled 1800 people that use the product and took the S. A. T. And they found that the mean math score was 518 which appears to be a little bigger. And we're testing at the 10% level of significance if in fact they did improve their statistically improve their uh math test scores. So the first part is to state what are null hypotheses are, and there's always equality with the mean Or with a new hypothesis, some musicals 14. And then the alternative would be μ is greater than 514 because it's increasing the score. So we do that and let's go ahead and do it in the calculator, because it will be a little quicker this way, we're gonna do a Z test since we actually know what the population standard deviation is. The hypothesized values. 514. Population standard deviation 113. The X. Bar. The sample mean was 518. The sample size is quite large, 1800. And then our alternative is that it increases greater than And we calculate and we get a test statistic of 1.502 with the p value of about .067. Okay, so let's write those down and let's analyze them. So 1.502 and 0.67 which is less than alpha phi alpha was 0.10. So I would reject h not in this case or reject the null hypothesis. So it does in fact look like this product did you know statistically improve a math scores. Now? Is there any practical significance? Does the impact of the score change? Have any significance? I would say no. You know that if this were the A. C. T. And you went up four points. Yeah I mean that's pretty good. But with the S. A. T. Considering the entire scores 1500 points or 1600 points. In fact with writing I think it's 2400 points. Like four points really isn't that much so practical significance you just sort of use your logic. That's not a whole lot of increase. So now if we do it with just everything else is the same. But we just decrease that sample size to 400. What happens? Let's go back to Staten tests And you know like I said all this stays the same except we change this to 400. Let's see how That changes things. So look at that .708. And the P value is already .224 basically. So the z would be .708 and then the p value of .239 which is greater than alpha. The office still appoint 10. So I would fail to reject object. It's not so basically as and increases um and all else being the same. The P value can decrease substantially.