Use the following data for the Questions 3 ID GenderAgeReligion Income 32 37 72

Question

Use the following data for the Questions 3 ID GenderAgeReligion Income 32 37 72 86 30 32 29 29 53 68 72 $25,000 $20,000 $50,000 $75,000 $12,000 $45,000 $150,000 $35,000 $14,500 $65,000 $85,000 $20,000 4 10 12 Variable descriptions: ID - Respondent's identification number Gender - Respondent's gender 1 Male 2 = Female Age - Respondent's age Religion - Respondent's religious affiliation 1 = Protestant 2 = Catholic 3: Jewish Income - Respondent's income in dollars per year 3. The investigator wants to know if there are differences in a person's income based on what religious group they are affiliated with What are the null and research hypothesis for examining this? (2 points) e. f. What is the proper statistical test to use? (1 point) g. Is the test statistically significant? (1 point) h. Write one/two sentences that describe what you found when you ran the analysis. Remember, your sentence(s) should be descriptive so that someone reading your sentence(s) would understand what the research study is about and what the findings were. Remember that a complete sentence will include many parameters: means, standard deviations, r, t, and/or f values, degrees of freedom, and/or statistical significance. Not all of these parameters are relevant for all statistical tests. Be sure to provide the proper information for the statistical test that was chosen

Explanation / Answer

Question 3

Part e

The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: There is no any statistically significant difference in the average income of protestant, catholic, and Jewish.

Alternative hypothesis: Ha: There is a statistically significant difference in the average income of protestant, catholic, and Jewish.

H0: µ1 = µ2 = µ3 versus Ha: at least two µ’s are different.

Part f

Proper statistical test for testing above hypothesis is the one way single factor analysis of variance or ANOVA F test for checking significant difference in more than two population means.

Part g

The required one way ANOVA F test is given as below:

Income

N

Mean

Std. Deviation

Protestant

4

50375

66655.05107

Catholic

4

50000

26770.63067

Jewish

4

48750

25617.37691

Total

12

49708.3333

39832.86579

ANOVA

Income_$

Sum of Squares

df

Mean Square

F

Sig.

Between Groups

5791666.667

2

2895833.333

.001

.999

Within Groups

1.745E10

9

1.939E9

Total

1.745E10

11

For this ANOVA table, p-value = 0.999 > = 0.05

So, test is not statistically significant.

Part h

For this test, we get P-value as 0.999 which is greater than the level of significance or alpha value 0.05, so we do not reject the null hypothesis that there is no any statistically significant difference in the average income of protestant, catholic, and Jewish. There is sufficient evidence to conclude that there is no any statistically significant difference in the average income of protestant, catholic, and Jewish.

Income

N

Mean

Std. Deviation

Protestant

4

50375

66655.05107

Catholic

4

50000

26770.63067

Jewish

4

48750

25617.37691

Total

12

49708.3333

39832.86579

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