Question

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Do graduates of undergraduate business programs with different majors tend to earn disparate average starting salaries? Is there any reason to doubt the equal variance assumption made in the one-way ANOVA model in this particular case? Support your response to this question.

Accounting	Marketing	Finance	Management
$31,450	$28,350	$29,325	$27,320
$35,650	$27,845	$29,550	$26,450
$32,630	$28,430	$31,640	$30,135
$37,110	$27,645	$32,760	$27,340
$29,440	$28,635	$30,550	$28,635
$37,330		$29,875
$30,835		$28,890
		$31,650

Answer 1

ANSWER;

Do graduates of undergraduate business programs with different majors tend to earn disparate average starting salaries? Consider the data listed .

a. Is there any reason to doubt the equal-variance assumption made in the one-way ANOVA model in this particular case? Support your response to this question.

In order to clear the doubt of the equal variance assumption made in On-Way ANOVA test in this particular case, Box plot can be made in Stat Tool using the following procedure as follows:

1. 1. Consider the data as shown in the screenshot given below:

   

2. 2. Select the whole data then go to Data Set Manager shown under the Stat Tools, and then a dialogue box will appear, Click Yes on it. Another dialogue box will appear, again click on Yes, in order to store this data on the Stat Tool.

   3. Then go to Summary Graph under Stat Tool, and under this select Box-Whisker Plot as shown in the screenshot given below:

   

3. 4. Then the given below dialogue box will appear, in this tick all the 4 types of Business majors as shown below:

   

4. 5. Click on OK in the above shown dialogue box, the output of the box-plot will be displayed o the new worksheet a shown below:

   

   From the side-by-side box plot obtained above two things are clear. First there is little doubt that students with Marketing major tend to have lowest starting salary than the students doing majoring in Management, Finance and Accounting. Secondly it can be clearly seen that the equal variance assumption is grossly violated here. There is very little variation in starting salary of studing doing majoring in Management and a large amount of variation in the starting salary of the stuents who are doing majoring in Accounting.

   In order to decide whether to reject the hypothesis that the mean starting salary is same for each of the given buiseness majors at 10 % significance level or not, following statistical test can be set up as follows:

   The Null Hypothesis will be that there is no difference in the mean starting salary for each of the given buiseness majors that is:

   

   Here is the mean starting salary of the business major. And the Alternative Hypothesis will be that there is significant difference in the mean starting salary for each of the Business major.

   To perform this test in Stat Tools following is the procedure:

   1 Consider the data as shown in the screenshot given below:

   

5. 2. Select the whole data then go to Data Set Manager shown under the Stat Tools, and then a dialogue box will appear, Click Yes on it. Another dialogue box will appear, again click on Yes, in order to store this data on the Stat Tool.

   3. Then go to Statistical Inference and under this select One-way ANOVA as shown in the screenshot below:

   

6. 4. The dialogue box which is shown below will appear, in this tick on all the 4 Categories of the Business majors and select 90% confidence interval from the drop down menu as shown below:

   

7. 5. Click on OK in the above shown dialogue box, the One-Way ANOVA output will be displayed on the new worksheet as shown below:

   

   Thus by looking at the obtained above in the output summary of One-Way ANOAVA test, it can be said that there is evidence to reject the Null Hypothesis, because on comparing this value with 0.05, it is found that which is very less than 0.05, which is the condition for accepting the Alternative Hypothesis, so it can be

8. rejected at 10 % significance levels that the mean starting salary is same for each of the given business majors

   In order to check which pairs of differences between the means are statistically significant at the 10 % confidence interval, first it is needed to construct 90% confidence intervals for all the pairs which can be done in Stat Tools as follows:

   In step 4 in the procedure explained in part b. the dialogue box which is shown below, tick on all the 4 business majors and under Confidence Interval Methods, tick on Turkey Correction and select 90% from the drop down menu under Confidence Interval as shown below:

   

9. After Clicking on OK, the table of the confidence intervals which is shown below will appear in addition to the output summary which is obtained in part b.

   

   From the Confidence intervals of all the pair of differences between the means obtained above, it is observed that the pairs, Accounting-Marketing, Accounting-Finance, Accounting- management are statistically significantly at 10 % significance level because they are coming out to be all positive and thus with high confidence it can be said that the two means in the pair are not equal. Thus there is very strong evidence to reject the Null Hypothesis