Question

1. Restate the question that the researcher is investigating?

2. What type of test is appropriate for this question?

3. Write out the model statements in words (make sure you include null model too)

4. What are the hypotheses (all of them)

5. Run the appropriate statistical test in Minitab (for this example you do not need to check for normality, variance, outliers etc, just run the test). Paste the output here. Paste it so it is easy to read.

6. Run a post-hoc test if appropriate. Paste results here as appropriate.

7. Summarize what the results are telling you. What is the take home message that you want to tell your audience. (I am not requiring a final graph for this assignment)

Salary course   Subject
1700 Humanities
1900   Humanities
1800 Humanities
2100 Humanities
2500   Humanities
2700   Humanities
2900   Humanities
2500   Humanities
2600   Humanities
2800   Humanities
2700   Humanities
2900   Humanities
2500   Social Sciences
2300   Social Sciences
2600   Social Sciences
2400   Social Sciences
2700   Social Sciences
2400   Social Sciences
2600   Social Sciences
2400   Social Sciences
2500   Social Sciences
3500   Social Sciences
3300   Social Sciences
3600   Social Sciences
3400   Social Sciences
2700   Engineering
2800   Engineering
2900   Engineering
3000   Engineering
2800   Engineering
2700   Engineering
3700   Engineering
3600   Engineering
3700   Engineering
3800   Engineering
3900   Engineering
2500   Managament
2600   Managament
2300   Managament
2800   Managament
3300   Managament
3400   Managament
3300   Managament
3500   Managament
3600   Managament

Answer 1

Restate the question that the researcher is investigating ?

Answer : researcher wants to test or to find there is mean difference between treatments, it is significant or not

that is treatments are significant or not here treatments are subject.

## Q ) What type of test is appropriate for this question ?

we can use ANOVA test : and find out treatments are significant or not here treatetmes are subject .

also find out which treatment is different .

## Q ) Write out the model statement in words : Yij = u +  α i+ error  

Ho : all treatments mean are same (null hypothesis ) vs H1 : at least one mean is differ for treatment.

Yij = u +  α i+ error ( model )

where u is overall mean , alpha is treatments .

## Q) what are the hypothesis :

Ho : null hypothesis : all treatments means are equal vs

H1 : alternative hypothesis : at least one mean is differ

## Q ) Run the appropriate statistical test in Minitab  Paste the output here. Paste it so it is easy to read.

Answer : paste here output of the minitab:

One-way ANOVA: salary cource versus Subject

Method

Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor Levels Values
Subject 4 Engineering, Humanities, Managament, Social Sciences

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Subject 3 4167567 1389189 6.23 0.001
Error 41 9144878 223046
Total 44 13312444

### from anova p value is less than alpha value hence we reject Ho ( using p value appraoch)

we can say that there is enough or sufficient evidence to conclude that there is atleast one treatment is differ .

that is atleast one subject mean is differ

Model Summary

S R-sq R-sq(adj) R-sq(pred)
472.277 31.31% 26.28% 17.15%

Means

Subject N Mean   StDev 95% CI
Engineering 11 3236 495 (2949, 3524)
Humanities 12 2425 435 (2150, 2700)
Managament 9 3033 485 (2715, 3351)
Social Sciences 13 2785 478 (2520, 3049)

Pooled StDev = 472.277

## Q ) Run a post hoc test if appropriate . Paste results here as approapriate

answer : post hoc test is valid only if we have reject Ho : by using it we can find which treatment mean is differ .

here post hoc test is valid because we reject Ho .

Tukey Pairwise Comparisons

Grouping Information Using the Tukey Method and 95% Confidence

Subject N Mean Grouping
Engineering 11 3236 A
Managament 9 3033 A
Social Sciences 13 2785 A B
Humanities 12 2425 B

Means that do not share a letter are significantly different.

Tukey Simultaneous Tests for Differences of Means

Difference SE of Adjusted
Difference of Levels of Means Difference 95% CI T-Value P-Value
Humanities - Engineering -811 197 (-1340, -283) -4.12 0.001
Managament - Engineering    -203 212 ( -772, 366) -0.96 0.775
Social Scien - Engineering -452 193 ( -970, 67) -2.33 0.107
Managament - Humanities 608 208 ( 50, 1166) 2.92 0.028
Social Scien - Humanities 360 189   ( -147, 866) 1.90 0.243
Social Scien - Managament -249 205   ( -798, 300) -1.21 0.621

Individual confidence level = 98.94%

using p value appraoch result is not significant if p value is less than alpha value here

using p value approach . Humanities - Engineering ,and Managament - Humanities mean pair is significant out of all .

## Q ) Summarize what the results are telling you . What is the take home mesasge that you want to tell your audience .

Answer : first from anova reuslt is significant and there is at least one treatment mean is differ .

use post hoc test ( Tukeys comparison test and find which one is differ )

overall we can say that subjects ( tramtments ) have different with salary course  .and

Humanities - Engineering ,and Managament - Humanities mean pair is significant out of all .