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A developmental psychologist is examining the development oflanguage skills from age 2 to 4. Three different groups ofchildren are obtained, one for each age, with...

Question

A developmental psychologist is examining the development oflanguage skills from age 2 to 4. Three different groups ofchildren are obtained, one for each age, with n = 16 children ineach group. Each child is given a language-skills assessmenttest. The resulting data were analyzed with an ANOVA to testfor mean differences between groups. The results of the ANOVAare presented in the following table. Fill in all missingvalues. (A step by step process is not needed for thisproblem). Source

A developmental psychologist is examining the development of language skills from age 2 to 4. Three different groups of children are obtained, one for each age, with n = 16 children in each group. Each child is given a language-skills assessment test. The resulting data were analyzed with an ANOVA to test for mean differences between groups. The results of the ANOVA are presented in the following table. Fill in all missing values. (A step by step process is not needed for this problem). Source SS df MS Between treatments 20 ________ _______ F =_______ Within treatments _______ ________ _______ Total 200 ________



Answers

Many college and university students obtain summer jobs. A professor wanted to determine whether students in different degree programs earn different amounts. She randomly selected five students in each of the 3 university programs and asked them to report what they earned the previous summer (in thousands of dollars). The following partially filled-in ANOVA table was obtained. Fill-in the rest of the table. (Use exact values for df and round all other numbers to 2 decimal places, if needed.)

Okay, so here let the null hypothesis would be it's not after and this is a um one will be equal to m times me too. Okay. And there is no difference between the means of the uh two treatments A and B. Okay. And the alternative to have parties a little added here. Okay, so it will be clear and this is him times Me too. Okay uh And this is equal to me one. Okay? And the alternative hypothesis, uh it will be, me one will be not equal to a mewtwo. Okay. And there is no difference between the mean of the two treatments in B. Okay. Now, in part two we are given that K is equal to two and Alpaca is up 10 vibe. Okay? And the p value is calculated by f is equal to nine. this p value is So so par degree of freedom is equal to one and a degree of freedom 1 uh uh Two is six. Okay, so para critical value, it is calculated that alpa is uh uh so we are degree of freedom is uh so let let write it here. Right, so let's clear it. Ah Let or mean is who are mean is ah And this is equal to 12 plus 24 divided by eight. Okay, and this is 36 divided by eight. So this is 4.5. And the degrees of freedom one is came in as one, so this will be two minutes when this is one. Okay and the ss treatment is let the ss treatment will be ah the ss treatment is equal to the sum up end times, expat up I. Menace overall, overall mean square. Okay, so this is equal to four times three minutes. 4.5 whole square plus four times six minutes 4.5 whole square. Okay, So this is equal to four times menace. sq plus four times one point pipe squared. Okay, so this is four times 2.25 plus four times 2.2 points. Okay, so nine plus uh nine will be equal to 18. All right. And ah M. S. T. R. Is equal to ss and this will be equal to treatment Divided by degrees of Freedom one. So this is 18 divided by one. This is 18, right? And the ss arab is equal to some times the sum of squares. Okay, sum up square. So this is a poor plus eight. This is 12. Right? And the degrees of freedom to this is equal to n menos que Right? And ah in his administered to a six. So, the M. S. Error is and this is equal to the essence error. Okay. Do you want me by degrees of freedom to Now this will be equal to 21 by six? So this is two, right? And uh a P is equal to M. S. T. R, divided by M. S. E. Right? So this will be equal to 18 to everybody to this is nine. Right? And uh so f is equal to nine now? Uh Mhm. A little added here. Right? So this is the source. This is N. O. R. So this is between Okay. And this is written. So this will be more easy. Right? And this is total. All right. So this is S. S. And this is degrees of freedom. And this is mean square, mean square and Epp and eps Cv and P. Right? So this is 18. This is 12 and the total is 30 30 And d. as 1 6 and seven uh 167. Right. And the main square is 18 two and it is nine and ah FcV is 5.98 74. Okay. And P S 010 to 40. So and three. Uh So the decision is so since it test uh is yeah write it here. So, a test ah uh This is uh this uh mhm. Uh This is greater than a critical right. Greater than A critical of 5.98. So then we reject each night. We reject we reject that's not okay now. So also let the ap test is greater than a critical than we rejected snap. And also the P value is less than alpa. So then we rejected not. So by the decision are by the process of P value are with the ah ah let with the process of people. We also rejected because the value is Which is period a period of 0.02 pour zero, which is less than the Alpa. All right. So, we will also reject it. Not here now. Uh Uh so in part for our conclusion is so there is a sufficient evidence at 95% level of significance to conclude that uh there is a difference in the means of the two treatments, right?

This particular question. They said that all the soldier compares the average I Q score. So we have a sword. George. Okay, was combating the average I Q score off the force born children with the average i Q off their younger siblings were. So we're having comparison from seeing the post born children. Okay, we're comparing them with the younger single limbs. We're comparing the ICU School of Border than so the children are randomly selected from the public schools in a school district. Your onda, we compare. So is any compares 400 pairs off kitchen strong the torture and families. Okay, Now we see that the schools that I just did for a judge All right, so the other siblings average 29 disasters are data given it wasn't a question. And this is the standard deviation off. Then that is Ah, the younger siblings evident 28. And, uh, this is with a standard deviation. Or then again, so the undocumented going to comment on the use of statistical our tests over here, and this is one of the final conclusion for this particular problem. So I'm going to write down that this is knock er for example, desk. All right, Onda. He's noticed that the bad siblings, they are not toe independent groups. I would rather see that they are dependent measures because, uh, the I Q scores between the siblings is north independent. All right. And you also see that the design that should have been used is, uh, a matched there study for dependent samples. So there is no way that we are going to have compared in between these two examples and therefore we say that we could not you was to sample design for this particular experiment door study.

In exercise 12. We're going to be estimating the speaking vocabulary of three year old Children in a particular socioeconomic class. Mm So we're given that a sociologist studies the speech of four Children and that tells us that the sample size n his fault and the sociologist determines that the mean and standard deviation for that sample are 120, And 215 Watts, respectively. So X bar Equals 1120 watts and s equals 215 Watts. No, we shall be assuming that speaking vocabularies are normally distributed. And then use this information To construct an 80% confidence interval for the mean speaking vocabulary of all three year old Children in this socio economic group. So 80% confidence interval four. The population means. Now the first thing is to determine the formula that is needed. Uh Which in this case is X. Bar class or minus critical value of T. For the given level of significance to multiply by as over discourage them. No, We want alpha. The level of significance, it's equal to 1 -0.8. Now equals 0.2. When we have that, it's going to become 0.1. Since this is a T distribution, we need to get the degrees of freedom using N -1 and that's going to be 4 -1. And that's equals three. So the critical value of T corresponding to the 0.1 level of significance and 13° of freedom Equals, I'm sorry, 3° of freedom equals 1.638. So now we're ready to substitute the values that you have obtained and what we have been given into the formula. So expo 1120 plus or minus T value, which is 1.638, multiplied by S 215 Where by the Square of four. So when you simplify the margin of error using a calculator, you obtain 176 0.0 sniper. So We are 80% confidence that they mean speaking vocabulary of all three year old Children in this social economic group lies within uh range specified by this confidence interval.

Hi I'm David and I'm here you have your answering your question. Now let me bring up your question here. Any questions going to fill up the end of the table and in this one here we are given that the treatment in has the three University programs means that we go to three and then we have the belief five students for each then found him in. He called you The three times 5 and equal to the 15. And now let me try to live on the Empty some being one two, three for five, six and seven. Now let me try to find the first. Uh let me try to find the missing sale. We made our first one and the great freedom from the treatment. Then we'll echo to the The number of the categories here and then -1 And therefore we have to go to the 3 -1 and negative ju and then they Next one I want to five it will be the number three and the decree freedom on the daughter Every Echo Children to do. And we -1. So we have equal to 15 -1. And we go to the fourth thing and then the degree of freedom followed to the creative freedom on the era. There we go to the end minus guy And then we get this on Echo to the 15 3 -3 and Echo to the trial. And then for the Number four, once you find some of square in the era and we could use some subscribed the doctor man is sum of square the treatment and I felt we get equal to the 24.31 strip 0.3 and eco june the trail And next one the # five. I want to find the mean square error on the treatment. They were equal to the sum of the square of the treatment of a degree of freedom. So we have to go to the trump on 3/2. Then we get to go to The 6.15. and next we will have the number six the mean square error of uh and then we have the same subscribed the era of the degree of freedom on the era. They were echoed to the ground running by trial and look at you one and then the last one we will have the seven. So we have here will be 6.5. There will be one. The upstairs here we go to the mean square error. I'm the treatment of a mean square error. All right. And then we will have this one will be in the 6.15 the 1x1-6.15. And this will be the 6.15. And that will be in the over temple. We need to fill up here


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