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Bound students taking the standardized test follow normal Math SAT scores for all American college" distribution with the mcan 510 and standard deviation 95 . ...

Question

Bound students taking the standardized test follow normal Math SAT scores for all American college" distribution with the mcan 510 and standard deviation 95 . ccrtain college have the mean 490. Is there significant The scorcs of 12 randomly selected applicants evidence that the mean math SAT score of the applicants t0 this college lo wCt than average (that is, lower than 510)? this Z-cuSc OI f-case? Why? Can we safely upply our procedures? Why? State the null and altemative hypotheses Find

bound students taking the standardized test follow normal Math SAT scores for all American college" distribution with the mcan 510 and standard deviation 95 . ccrtain college have the mean 490. Is there significant The scorcs of 12 randomly selected applicants evidence that the mean math SAT score of the applicants t0 this college lo wCt than average (that is, lower than 510)? this Z-cuSc OI f-case? Why? Can we safely upply our procedures? Why? State the null and altemative hypotheses Find thc value of the test stalistic Find the P-value of the statistic , illustrate with skctch; and explain in words what means Do we have significant evidence that the Iean math SAT score of thc applicants this college 15 lowcr [han average? Les evidence reach the 5% signilicance level?



Answers

SAT Exam Scores A school administrator believes that students whose first language learned is not English score worse on the verbal portion of the SAT exam than students whose first language is English. The mean SAT verbal score of students whose first language is English is 515 on the basis of data obtained from the College Board. Suppose a simple random sample of 20 students whose first language learned was not English results in a sample mean SAT verbal score of $458 .$ SAT verbal scores are normally distributed with a population standard deviation of $112 .$ (a) Why is it necessary for SAT verbal scores to be normally distributed to test the hypotheses using the methods of this section? (b) Use the classical approach or the $P$ -value approach at the $\alpha=0.10$ level of significance to determine if there is evidence to support the administrator's belief.

In this question we want to test the null hypothesis and U equals 516 against the alternative hypothesis, mute is not equal 516. For example, data with and equals 20 X four equals 522. With a standard deviation of the population segment equal 114. Known at alpha equals 1140.1 confidence of this question is to ask your ability to perform a hypothesis test for population we knew where sigma is. No. The first question to answer is a why is it necessary the population normal? It's necessarily population be normal because you end less than 30. Since we don't have a sufficiently large sample, we must meet the requirement of normality for this. Has to be okay to complete. So proceeding on the tests, we first counted at the test net. This is a non equals experimentation unit which is 5 16 over segment we were talking in the numbers about gives 160.235 Next we can compute the critical value for alpha equals 0.5 from a Z. Table. This gives critical Z score plus or minus 1.645 That's we can include. Indeed, we reject a shot we fail to reject H not because, you know, it's not in the critical region. 0.235 is not less than negative 1.645 or greater than 1.645 Therefore it's not in the critical region.

In this question we want to test the null hypothesis and U equals 516 against the alternative hypothesis, mute is not equal 516. For example, data with and equals 20 X four equals 522. With a standard deviation of the population segment equal 114. Known at alpha equals 1140.1 confidence of this question is to ask your ability to perform a hypothesis test for population we knew where sigma is. No. The first question to answer is a why is it necessary the population normal? It's necessarily population be normal because you end less than 30. Since we don't have a sufficiently large sample, we must meet the requirement of normality for this. Has to be okay to complete. So proceeding on the tests, we first counted at the test net. This is a non equals experimentation unit which is 5 16 over segment we were talking in the numbers about gives 160.235 Next we can compute the critical value for alpha equals 0.5 from a Z. Table. This gives critical Z score plus or minus 1.645 That's we can include. Indeed, we reject a shot we fail to reject H not because, you know, it's not in the critical region. 0.235 is not less than negative 1.645 or greater than 1.645 Therefore it's not in the critical region.

Hi limit abortion here. The manager plans that you develop that the vehicles that the spokesman increases the sport of student. Right? So if you take population me Is 550. I mean this is 500 Kenya we have many politicians coming activity U equals that included the school. That means we have ordinary policies that is coming up to be you is better than 515 sample to simplify so to speak and sample me and samples and interviews so You know, there's a test. That hypothesis here at alpha is 0.10 no test hypothesis orders Oh and check that the means that that's 45 minutes to 19 significantly higher than by recipient. So let's go for that to find conspiracy that's coming up to be expanding them. You over and over then we put the values 5 19 -515 or we have the lemon over grew in number. We have the test statistic and this portion that is uh coming out to be 1.49. There will be 1.49 and is in technology when the p value for this. So people use coming up to be 0.0632 technology your point, you know six freedom. We have wildfires given and to the .1 they wanted it to be um livers less than alpha. Therefore we reject my hypothesis the project. Uh now about this nutcase. But that means the if you're the B part is a means to attack maps for or parliament is significantly higher than five. Everything. Yes it is because we accept the organism publicist So that is significantly higher. Yes, significantly higher for the part and write this significantly. Right. I'll see you back says I do think that the means that Max 45 and 19 was 500 people will affect the decision of a school admissions. And mr in other words that include the score have any particular significance. So we can say that the tea party you can get the score have the critical significant Because 5 90 significantly higher than 500 people. So people estimated to be Yes it has practical significance. If you go down to be bought Depart we have not just for this this board now and this time we have an S 400 for any for under the same statistics from this Yet for now temple we know 519 significantly more than 515 or no let's go for peace for that. That is coming up to be again we have expo negative mute or word now As over route 400 right. We put the same values here. And if I do not feed as politic for that. So that is coming up to be it will do We get to be 0.70 0.s send a little technology one of the Value P. So be the less than 0.235 0.23 five alpha beta Significant level. That is given a 0.10. So peter let's not at this time not be always greater than others. So therefore we find to reject we I mean will be Jack no taliban offices this time to try to reject uh hypothesis. So it is not practically significant, not practically significant. So uh So we can say it is not significant. Temperament of 519 is now not significant as a Acting differently. More than 500 team. That's what you can go for your toe. Now, what can be concluded here example, Sympathizing increasing as n increases the likelihood of getting enough hypothesis, increases likelihood of nanny. But if you have a large samples tend to overemphasizes practically insignificant difference. Right? So has and increases the likelihood of the retinal images increases my work. Last sample tend to overemphasize practically increasing civilian different. Thank you.

So we have information about the 2005 math s A. T. So it is called Meth S a T. And then I'll subscript at math and we're told that it has a mean of 520 a standard deviation of 115 and that it is basically a normal distribution. It's not exactly normal, but it's very close to one. And in part, A. We want to know what is the Z score. If somebody scores a 7 20 what is their Z score? Well, there is these scores what they got, minus the mean divided by 1 15. And so we see that that difference is 200. So let's take 200 divided by 115. And we find out that that is 1.7 roughly four. And that means that the person scored 1.74 standard deviations above the mean mhm. On the other hand, let's go the other way that we know that someone has a A Z score of 1.5 or the person scored 1.5 standard deviations above the mean and with them we want to know what was the person score. So remember the Z score is how many standard deviations above or below the mean So we don't know this score. But we know that this is true. And so with this will be multiplying 1.5 this value times 115 and then adding to that by 220 and we find out that the score would be 692.5. Now you can't get a 0.5 on the test, so it's either going to be a 6 92 or a 6 93. And Park Si is doing a comparison and they're dealing with the 2012 exam. And we know that the, uh, the S A T, assuming that it was math again, had a mean for that year of 514 and the standard deviation of 117 very similar to the previous when we looked at and the A C t, on the other hand, as a much lower point total. But the mean that year was 21 with a standard deviation of 5.3, and we have one person who scored on the S a t so we'll do that in blue on the S A T scored a score of 700 and on the other hand, the person on the scored a score of 30 and we want to know, relatively speaking, did which one did better? So let's find out. So let's go through and figure out what this s a T Z value is how many standard deviations above the mean so 700 minus 5 14. Divided by 117. And let me get that left front to see 700 minus 5 14. Divided by 1 17, the C score is 1.59 So this person scored 1.59 Standard deviations above the me. Now let's look at what happens here. What's the Z score here? And we have 30 minus 21 divided by 5.3. And once again, I'll go left front to see 21 books. I'm sorry. 30 right. Minus 21 which I already knew it was nine. I don't know why I don't just put nine divided by 5.3 and I can't do that. 5.3 division in my head and I get this. See, value is 1.698 So this is approximately 1.70 Standard deviations higher. So this person, relatively speaking, did a better job compared to others. Because this person has a score that is 1.7 standard deviations higher than me. And this one is only about 1.6 higher than the main. So this one is the winner.


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