Mathematics, 26.02.2020 05:58 marelinatalia2000

A recent college graduate is in the process of deciding which one of three graduate schools he should apply to. He decides to judge the quality of the schools on the basis of the Graduate Management Admission Test (GMAT) scores of those who are accepted into the school. A random sample of six students from each school was taken. Basic statistics and an ANOVA table are provided below.

Source DF SS MS F P Variable N Mean StDev

Factor 2 47511 23756 8.61 0.003 School 1 6 646.7 47.6

Error 15 41400 2760 School 2 6 606.7 68.9

Total 17 88911 School 3 6 523.3 35.6

Assuming all assumptions hold, can he infer at the 10% significance level that the GMAT scores differ among the three schools?
Hypotheses:

Test Statistic P-value statement and p-value

Conclusions and Interpretation (i. e. make a decision and answer the question being posed in one sentence).

Given the F-critical value from the Bonferroni method is + 2.684 and that the pooled standard deviation is 52.54, which of the pairwise differences is significant? Calculate three test statistics to help you answer this question. No hypotheses or conclusions necessary.

Answers: 3

Show answers

Answers

Answer from: vicsmi6191

For this case after conduct the ANOVA procedure they got an statistic of:

F = 8.61

With a p value of :

$p_v =P(F_{2,15} 8.61) = 0.003$

Since the p value is lower than the significance level $\alpha=0.1$

We can reject the null hypothesis that the means are equal at the significance level provided.

$t = \frac{\bar X_i -\bar X_j}{s_p \sqrt{\frac{1}{n_i} +\frac{1}{n_j}}}$

For school 1 and 2 we have:

$t = \frac{646.7 -606.7}{52.54 \sqrt{\frac{1}{6} +\frac{1}{6}}}= 1.318$

For school 1 and 3

$t = \frac{646.7 -523.3}{52.54 \sqrt{\frac{1}{6} +\frac{1}{6}}}= 4.068$

For school 2 and 3 we have:

$t = \frac{606.7 -523.3}{52.54 \sqrt{\frac{1}{6} +\frac{1}{6}}}= 2.749$

So as we can see we have significant difference between the means of school 1 and 3, and school 2 and 3

Step-by-step explanation:

Previous concetps

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

Solution to the problem

The hypothesis for this case are:

Null hypothesis: $\mu_{1}=\mu_{2}=\mu_{3}$

Alternative hypothesis: Not all the means are equal $\mu_{i}\neq \mu_{j}, i,j=1,2,3$

If we assume that we have groups and on each group from $j=1,\dots,p$ we have n_j individuals on each group we can define the following formulas of variation:

$SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2$

$SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2$

$SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2$

And we have this property

$SST=SS_{between}+SS_{within}$

For this case after conduct the ANOVA procedure they got an statistic of:

F = 8.61

With a p value of :

$p_v =P(F_{2,15} 8.61) = 0.003$

Since the p value is lower than the significance level $\alpha=0.1$

We can reject the null hypothesis that the means are equal at the significance level provided.

For the other part we can calculate the 3 statistics with the following formula:

$t = \frac{\bar X_i -\bar X_j}{s_p \sqrt{\frac{1}{n_i} +\frac{1}{n_j}}}$

For school 1 and 2 we have:

$t = \frac{646.7 -606.7}{52.54 \sqrt{\frac{1}{6} +\frac{1}{6}}}= 1.318$

For school 1 and 3

$t = \frac{646.7 -523.3}{52.54 \sqrt{\frac{1}{6} +\frac{1}{6}}}= 4.068$

For school 2 and 3 we have:

$t = \frac{606.7 -523.3}{52.54 \sqrt{\frac{1}{6} +\frac{1}{6}}}= 2.749$

So as we can see we have significant difference between the means of school 1 and 3, and school 2 and 3

Answer from: Quest

the answer is a) y= 2 csc [0.5 (x+pi/2)]-1

step-by-step explanation:

Answer from: Quest

well if he bought them at 5 cedis each sold them at 7 cedis each then he would make a profit of 2 cedis of each book. if in total he made 150 cedis profit that means he sold 75 books. he lost 12 books at the start so that means he originally bought a total of 82 books.

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 16:40

The table shows the total distance that myra runs over different time periods. which describes myra’s distance as time increases? increasing decreasing zero constant

Answers: 2

Answer

Mathematics, 22.06.2019 01:50

What will be the end result for the taxpayer who filed his federal income tax return using the 1040ez form shown belowa he'll owe $173b he'll receive a refund of $173c he'll owe $3921d he'll receive a refund of $3921

Answers: 2

Answer

Mathematics, 22.06.2019 03:30

Eiko is wearing a magic ring that increases the power of her healing spell by 30%30\%30%30, percent. without the ring, her healing spell restores health points. which of the following expressions could represent how many health points the spell restores when eiko is wearing the magic ring?

Answers: 2

Answer

Mathematics, 22.06.2019 04:30

In chemistry,n molecules of an ideal gas have pressure, volume, and tempersture that stand inthe following relation, where r is constant. solve the equation for n,the number of molecules. pv=nrt

Answers: 2

Answer

You know the right answer?

A recent college graduate is in the process of deciding which one of three graduate schools he shoul...

Questions