Does the mean collegiate GPA differ by residential Region at a 5% level of signi

ID: 3224725 • Letter: D

Question

Does the mean collegiate GPA differ by residential Region at a 5% level of significance?

A. State the claim.

B. State the test used and any necessary assumptions to conduct the test.

C. State the hypothesis in words relating to the question and as symbols.

D. State the probability distribution used to find critical values.

E. State the test statistic(Value)

F. State if you reject or fail to reject the null hypothesis, support with p-value or traditional test.

G. State your conclusion in terms of the claim.

h. Determine if there is a chance of a Type I or a Type II error, then state what the possible error may be in terms of the question.

Number Participa GPA of years In Support! Before HS | ACT | Collage I took to Residential upport Sub izctl SFA | Score PA Graduatel Region Program | Services 5.5 3.61 N N N N 1.65 141 21 63 2.36 243 16 13.771 29 N 17 | 2.511 21 3.5 2.64 19 13.371 25 2.51 5.5 1.97 21 | 3.15 21 3.40 2311 26 N N 45 267 26 13.431 23 N 1.85 4.5 N 2.19 N 35 13.431 21 1.93 38 | 3.57| 31 741 21 5.5 ide eg B | C | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 21-25 21 | | | | | | | | | | | | 21-18-28-31-21 -2-3-4-567R-10 1-12 3 | 4-5-67a1 20-21 2 23 24 25 26 27 28 29 3 31 32 3 3 3 36 37 38 9 40

Explanation / Answer

Solution:

Part a

Here, we have to check the claim or hypothesis whether the average collegiate GPA is differ by residential region or not.

Part b

The test used for the given scenario is the one way analysis of variance or single factor ANOVA F test for the significant difference in the population means. We assume that the data is coming from the normally distributed populations.

Part c

The null and alternative hypotheses in words are given as below:

Null hypothesis: H0: There is no any significant difference in the average collegiate GPA for the three different residential regions.

Alternative hypothesis: Ha: There is a significant difference in the average collegiate GPA for the three different residential regions.

The null and alternative hypotheses in symbol are given as below:

H0: µ1 = µ2 = µ3 versus Ha: µ1 µ2 µ3

Part d

The probability distribution used for finding the critical values is F distribution.

Part e

The ANOVA table for the given test is summarised as below:

ANOVA: Single Factor

SUMMARY

Groups

Count

Sum

Average

Variance

Region A

32.12

2.676667

0.181788

Region B

43.4

2.893333

0.268724

Region C

38.47

2.959231

0.328374

ANOVA

Source of Variation

P-value

F crit

Between Groups

0.543805

0.271903

1.036909

0.364623

3.251924

Within Groups

9.702292

0.262224

Total

10.2461

The test statistic value is given as F = 1.036909

Part F

We are given level of significance = alpha = 0.05

We have P-value = 0.3646

Here, P-value > Alpha

So, we do not reject the null hypothesis

Part G

There is sufficient evidence to conclude that there is no any significant difference in the average collegiate GPA for the three different residential regions.

Part h

There is a chance of a type II error which is the probability of do not rejecting the null hypothesis even though it is not true.