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0iWhich ofthe following description for research . study comparing problem- solving Is the correct scores obtained for 3 different age groups? Ir :OH 42 _ Ir :OH 42...

Question

0iWhich ofthe following description for research . study comparing problem- solving Is the correct scores obtained for 3 different age groups? Ir :OH 42 _ Ir :OH 42 = 0 02 > Zr < Ir :OH Two separate samples each with n 10 individuals receive different treatments: After treatment,the first sample has SS = 1740 and the second has SS 1620.The Mi-Mz = 8. Usc D ue .05 and two-tailed test (8pts). =|0 S1 (2 pts) SS @hLI = Hi = VzEo (2 pts) 116-1-9 SS =lbzo df = (2 pts) 8 Zw- 07 '10-1295 M

0 iWhich ofthe following description for research . study comparing problem- solving Is the correct scores obtained for 3 different age groups? Ir :OH 42 _ Ir :OH 42 = 0 02 > Zr < Ir :OH Two separate samples each with n 10 individuals receive different treatments: After treatment,the first sample has SS = 1740 and the second has SS 1620.The Mi-Mz = 8. Usc D ue .05 and two-tailed test (8pts). =|0 S1 (2 pts) SS @hLI = Hi = VzEo (2 pts) 116-1-9 SS =lbzo df = (2 pts) 8 Zw- 07 '10-1295 M +/ 3,40 Critical Region (2 pts) 6= *05" 93( L9' 1740 +Ibze _ 3360 01 87 = SS+S32 18



Answers

Using Table G, find the critical value(s) for each. Indicate the noncritical region or regions, and state the null and alternative hypotheses. Use $\sigma^{2}=225 .$ a. $\alpha=0.10, n=14,$ two-tailed b. $\alpha=0.05, n=27,$ right-tailed c. $\alpha=0.01, n=9,$ left-tailed d. $\alpha=0.05, n=17,$ right-tailed

In this problem. Our night hypothesis is given its not sigma squared equal to 25. Since this is like think best, our alternative hypothesis will be actual Sigmund greater than 25 It then you have forgiven to a 0.0. So this region shaded region will p 0.0. But now the grease off freedom equal toe end minus where and is given to be 17. So degrees of freedom equal to 17 minus one which is equal to 16. We don't now find the critical value in the table for Cascade distribution. We will see and I'll fight with 20.1 and degrees of freedom equal to 16. So the quiet kid total value is tactic to as seen in the day before the chi Square distribution. The shaded region is our critical future. So the angina region is a word, not critical region. Now, for this second problem, that man hypothesis is same. That this it's not, is Sigma squared equal toe to 25 as it this left and test our I've done anything hypothesis. A 20 basic musk were less than 25. The valuable finds given to be 0.0 to fight. So this shaded region is 0.0 proof. But now the grease off freedom equal toe end minus one. Anything you want to be 20. So degrees of freedom equal to 20 miners, one which is equal to 19. We have to now find that critical than you to find the critical value. Since it is nectar Test village, see under a fi quote one moment, See opens. You do fun that this V C under Al fight equal to 0.975 and degrees of freedom equal to 19. So the required critical value is 8.907 as seen in the table for the Chi square distribution. The shaded region is our critical region. So this actually region is over. Non critic, noncritical region. For this heart problem, our null hypothesis is given to be sick. Master equal toe 25. Since this is shortened, test our alternative Hepatitis is a June Bilby Sigma squared not equal to 25. The value of all finds given to be 0.0. As this is student test, the value of all five will be split into two parts that is alphabet to equal to zero point C over divided by two is equal to 0.5 will be this left side stated region and 0.5 will be this right side shaded region. Now the grease off freedom equal tow n minus one and it's given Toby talking. So degrees of freedom equal toe thought in minus one, which is equal to 12. We don't know. Find the critical values for, like sex critical value, see Under and Phi quartile 0.5 and degrees of freedom equal to 12. So the quite critical value is three point the quite critical injuries during the 8.300 as seeing in the table for the chi square distribution for Lex sex critical value V C and a fight with one minus 0.5 that this we will see under Al fight equal to 0.995 and degrees of freedom he called to plant. So the next X critical value is 3.7 food as seeming the table for the chi square distribution. Now they know that the region to the right side off the rights. It's critical value and to the left side often excites critical value. That is, the shaded region is over freethinker region. So this actually region is our not critical region. Now our nine hypothesis h not is Sigma's critical due to 25 since it this left leg test Our alternative hepatitis is actually will be Sigma squared less than 25 the valuable face given to be 0.2 fat. So this shaded region is 0.2 fat Now the degrees of freedom equal toe end minus one and is given Toby 29. So the grease off freedom equal to 29 minus one which is equal to 28 even now find that critical for you. Since this is next think test, we will see under our fight will one minus 0.2 Fact that this BBC under al fight equal to 0.975 and the grease off freedom equal to 28. So the quite critical value is 15.308 as seen in the table for the chi Square distribution. Now we know that the region to the left off the left sites critical value that is, the shaded region is our critical Egypt. So this actually region is a lot nor pretty good teacher.

So we would be assuming that the ratings for the females is equal to the ratings for the males. And alternately we just want to know if there's a difference. So we would do and not able to and use a two tailed tests. So I always like to draw a picture. And so we're going to assume that the difference between males and females is zero and we're actually getting a difference that's negative, what we're doing to tell tassel we're getting a difference that's negative, but then we'll symmetrically go on the opposite side and these two together will be R. P. Value. Now I use the software to find how the degrees of freedom and it ends up, the degrees of freedom comes out to be 13.77 And I put all my data in the calculator and into two lists. And I found that the mean of the first group of the females was 4.2 and the mean of the males was 4.1. And then divided by, we had the standard deviation of the females being 0.7 to roughly one square divided by the sample size which was 10. And then the males was 0.35 28 squared divided by a sample size of again 10. And when I got that test statistic that test statistic came out to be negative 0.315 So it was very close, it was actually way up here and then symmetrically so that P value we can see is very large. And so two times the probability of getting a test statistic with 13.77 degrees of freedom being less than or equal to this value. That p value comes out to be about 75 76% 760.756 Excuse me 0.7576 And so we fail to reject the null. Mhm. Therefore it appears as though the ratings for our males and females here to be the same. Mhm.

In this problem, we are asked to determine the critical values for several hypothesis tests about the difference between two means with unknown population variances. So for parts A three D were given the alternative hypothesis. We're given the sample sizes for two samples that are used to test the hypothesis and were given the significance level Alfa. And another thing to note is we're told that the population variances are unknown, which means the difference of our sample. Averages are sample means are distributed according to the T distribution, and so the critical value is based on the T distribution. So for part A, we have a no hypothesis new one minus mewtwo not equal to zero. We have and one is equal to 26 and two is equal to 16 and Alfa is 0.5 So we can look are critical value up in the tea table based on this information. But first, let's find the degrees of freedom. Since we're calculating manually, we're just going to take the smaller sample size and subtract one. So that is 15 and we're also going to note that the alternative hypothesis is, ah, not equal to hypothesis which means that this is a two tailed test, which means that an area of 0.5 it's distributed into both the upper and lower tail of the distribution. So looking this up, we have 15 degrees of freedom, an area of 0.5 and two tails. So are critical. Value is 2.131 and I've made a positive remind us 2.131 because for a two tailed test, we're looking for critical values. So let's say this is positive 2.131 and this is minus 2.131 in the two tailed test. We're going to reject the null hypothesis if our test statistic falls within the critical region in either tail. And so we're looking for test scores that are greater than 2.131 or less than minus 2.131 And for part B. So I'm not gonna write out all the information for Part B. It's just it's an alternative hypothesis of new one. Minus mewtwo is less than zero, so this is a lower tail test. The smaller sample sizes and two is equal to 27. So the degrees of freedom is 26 and the significance level is 0.1 So it's a lower tail test, which means that we're looking for an area of 0.1 in one tail, and the degrees of freedom is 26 and so are critical. Value is minus 2.479 and that's minus because this is a lower tail test. And that's based on the sign in the alternative hypothesis that we're looking for something less than zero. I thought the alternative hypothesis is that new one minus mewtwo is less than zero, so we're interested in the lower tail of the distribution. And for part C, the alternative hypothesis is new. One minus you, too, is greater than zero. The smaller sample size is and one which is eight, which means that the degrees of freedom is seven. Alfa is 0.10 so this is an upper tail test. New one minus mewtwo is greater than zero, so it's seven 0.10 in one tail, and that gives 1.415 And that's positive, since it's an upper tail test and then for party. The alternative hypothesis is mu one minus. Mewtwo is not equal to 10 and we have a smaller sample. Is is en one, which is 14. So that implies the degrees of freedom is 13 and the significance level is 0.5 So again, the alternative hypothesis is new. One minus mewtwo is not equal to 10 so you can have a night prosthesis on the difference of means being not equal to zero are greater than zero are less than zero or any other number it doesn't actually change with. The critical value is it would change with the test statistic comes out as. But it doesn't change the problem in terms of the critical value once it's been standardised to the T distribution. So this is just, ah two sided test again. So going to the tea table, we have 0.5 in two tails then with 13 0.5 and two tails, gives us 2.160 plus or minus 2.16 year old

In this problem we're gonna be using the two proportion plus four Z interval procedure to write our 80% confidence interval. So r two p hats are going to change the number of successes need to get one added to each of them. So we're going to have 11 successes in Group 1, 19 successes in Group two. With a sample size of 22 from Group one and 32 from Group two. And when I convert these into decimals, sample proportion number one is 10.5, sample proportion number two is 20.594 And I've already plugged these in for P hat one and two in the formula below my new sample sizes are 22 32. Mhm. And now we'll figure out the margin of error which comes out to be 0.173 Yeah. And that's what we are going to add on and subtract from negative 0.94 And that will yield us our confidence interval. That's going to go from Yeah, negative 0.267 267 to positive point oh 79 Okay. And as we refer back to exercise 12.82 where the confidence interval was negative 0.28352 point oh 8349 Our new confidence interval is smaller, but it has the same center.


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