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Step 1: Find or collect a Dataset

For this project, you must find some sort of published, existing data. Possible sources include: almanacs, magazine, journal articles, textbooks, web resources, athletic teams, newspapers, reference materials, campus organizations, professors with experimental data, electronic data repositories, the sports pages or collect your own data from fellow students, neighbours or friends.

The dataset you select must have at least 25 cases. It also must have at least two categorical variables and at least two quantitative variables. Choose or collect a dataset that interests you!

Step 2: Analyse Your Data!

See the description below of what analysis should be included. Use technology to automate calculations and graphs.

Step 3: Write Your Report

Cut and paste all relevant computer output with your analysis. Be sure to include both computer output and your discussion of that output in every case. As you discuss each analysis, be sure to interpret what you are finding in the context of your particular data situation. Include all of the following.

How did you find or collect your data? (If you found the data, give a clear reference. If you collected the data, describe clearly the data collection process you used.) What are the cases? What are the variables? What population do you believe the sample might generalize to? Is the sample data from an experiment or an observational study?

Use one of these or come up with your own idea or find your own source. There are many sites reporting frequency counts from survey results.

  • Frequency of smoking (never, occasionally, frequently), gender for students, age of the student and number of years smoking etc.
  • Academic division (business, accounting, TESOL,...), whether the student has a Mac, PC, or neither, for students, age and number of trimesters completed.
  • Whether a person plans to vote in the next election, political party affiliation (yes or no), age and number of years affiliated with the party.
Research Hypotheses

The statistical analysis for the qualitative and quantitative variables is very useful in the process of checking and comparing different claims or hypotheses. Here, we want to check some claims and hypotheses regarding the qualitative and quantitative data. We have to use the descriptive statistics, inferential statistics or testing of hypothesis, graphical analysis for the variables included in the data set. By using the descriptive statistics we get the general idea about the nature of the data for the variables. By using testing of hypothesis we can conclude about the claim at the given level of significance. Also, we have to use graphical analysis which is useful in easy understanding of the concepts. Let us see this statistical analysis report in detail.

H1: There is no any significant difference in the average monthly income for the male and female.

H2: There is no any significant difference in the average monthly income for the persons with different education levels.

H3: There is no any significant difference in the average monthly expenditure for the male and female.

H4: There is no any significant difference in the average monthly expenditure for the persons with different levels of education

H5: The two categorical variables gender and education are independent from each other.

Statistical Analysis

In this topic, we have to see the descriptive statistics, inferential statistics and graphical analysis of the given data for the monthly income and expenditure of the persons. For the given study of statistical analysis, there are two qualitative variables such as gender and education; and there are two quantitative variables such as monthly income and monthly expenditure of the persons.

First of all we have to see the frequency distribution of the gender of the persons in the given data set. The required frequency distribution is given as below:

Gender

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

Male

28

56.0

56.0

56.0

Female

22

44.0

44.0

100.0

Total

50

100.0

100.0

There are 28 males and 22 females involved in the given data set. The frequency distribution for the variable education is given as below:

Education

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

High School/Under-graduate

15

30.0

30.0

30.0

Graduate

16

32.0

32.0

62.0

Post-graduate

19

38.0

38.0

100.0

Total

50

100.0

100.0

There are 19 post graduate persons, 16 graduate persons and 15 under graduate persons in the given data set.

Now, we have to see the descriptive statistics for the two quantitative variables such as monthly income and monthly expenditure. The required descriptive statistics is summarised as below:

Descriptive Statistics

N

Minimum

Maximum

Mean

Std. Deviation

Monthly income in AU$

50

4096.00

7897.00

5940.5800

952.45903

Monthly expenditure in AU$

50

2718.00

6536.00

4612.1800

980.83593

Valid N (listwise)

50

The average monthly income of the persons involved in the data set is given as $5940.58 with the standard deviation of $952.45903. The minimum monthly income is recorded as $4096 while the maximum monthly income is recorded as $7897. The average monthly expenditure is given as $4612.18 with the standard deviation of $980.83593. The minimum monthly expenditure is observed as $2718.00 while the maximum monthly expenditure is observed as $6536. The box plot for the monthly income of the persons is given as below

The box plots for the monthly incomes for the male and female is given as below:

From the above box plots, it is observed that the average income for the male is greater than female. There is more variation in the monthly income for females. The descriptive statistics for the monthly income for the male and females is given as below:

Group Statistics

Gender

N

Mean

Std. Deviation

Std. Error Mean

Monthly income in AU$

Male

28

5929.9286

897.47563

169.60695

Female

22

5954.1364

1039.62046

221.64783

Statistical Analysis

From the above table, it is observed that the average monthly income for the male is given as $5930 approximately while the monthly income for the female is given as $5954.

Now, we have to use the inferential statistics or testing of hypothesis for checking the claims regarding the variables included in the given data set.

Here, we want to check the hypothesis or clam whether there is any significant difference in the average monthly income of the male and female or not. For checking this hypothesis, we have to use two sample t-test for the population mean. We will consider 5% level of significance for this test. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: There is no any significant difference in the average monthly income for the male and female.

Alternative hypothesis: Ha: There is a significant difference in the average monthly income for the male and female.

The required t test is given as below:

Independent Samples Test

t-test for Equality of Means

t

df

Sig. (2-tailed)

95% Confidence Interval of the Difference

Lower

Upper

Monthly income in AU$

Equal variances assumed

-.088

48

.930

-575.41678

527.00119

Equal variances not assumed

-.087

41.679

.931

-587.57397

539.15838

For this test, the p-value is given as 0.93 which is greater than the given level of significance or alpha value 0.05. We know that if the p-value is less than the given level of significance or alpha value, then we reject the null hypothesis and if the p-value is greater than the given level of significance or alpha value, then we do not reject the null hypothesis. Here, we get p-value is greater than the given level of significance or alpha value 0.05, so we do not reject the null hypothesis that there is no any significant difference in the average monthly income of the male and female.

Now, we have to see the box plots for the comparison of the monthly income of the persons based on the education which is given as below:

Now, we have to check another claim or hypothesis whether there is any significant difference between the average monthly income for the persons with different education qualifications. For checking this claim, we have to use the one way analysis of variance or single factor ANOVA. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: There is no any significant difference in the average monthly income for the persons with different education levels.

Alternative hypothesis: Ha: There is a significant difference in the average monthly income for the persons with different education levels.

We assume 5% level of significance for this test. The descriptive statistics for the monthly income of the persons based on the education level is given as below:

Descriptive Statistics

Monthly income in AU$

N

Mean

Std. Deviation

Minimum

Maximum

High School/Under-graduate

15

4834.4

617.2999

4096

5936

Graduate

16

6020.063

434.9119

5436

6967

Post-graduate

19

6746.947

551.2485

6010

7897

Total

50

5940.58

952.459

4096

7897

From the above table, it is observed that there is difference in the average monthly income of the persons based on the education level. The ANOVA table for this test is given as below:

ANOVA

Monthly income in AU$

Sum of Squares

df

Mean Square

F

Sig.

Between Groups

3.081E7

2

1.540E7

53.075

.000

Within Groups

1.364E7

47

290251.095

Total

4.445E7

49

For this ANOVA test, we get the p-value as 0.00 which is less than the given level of significance or alpha value 0.05, so we reject the null hypothesis that there is no any significant difference in the average monthly income of the persons with different education levels. There is sufficient evidence to conclude that the average income for the persons with different education level is not same.

Now, we have to see the box plots for the overall monthly expenditure for the persons and box plots for the monthly expenditure for the male and female which is given as below:

Now, we have to check another claim whether there is any significant difference in the average monthly expenditure in male and female or not. For checking this claim we have to use two sample t test for the population mean. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: There is no any significant difference in the average monthly expenditure of the male and female.

Alternative hypothesis: Ha: There is a significant difference in the average monthly expenditure of the male and female.

The descriptive statistics for the monthly expenditure for the male and females is given as below:

Group Statistics

Gender

N

Mean

Std. Deviation

Std. Error Mean

Monthly expenditure in AU$

Male

28

4580.5000

898.24164

169.75171

Female

22

4652.5000

1097.43041

233.97295

For this test we will assume 5% level of significance or alpha value.

The required two sample t test for the population mean is given as below:

Independent Samples Test

t-test for Equality of Means

t

df

Sig. (2-tailed)

95% Confidence Interval of the Difference

Lower

Upper

Monthly expenditure in AU$

Equal variances assumed

-.255

48

.800

-639.29274

495.29274

Equal variances not assumed

-.249

40.252

.805

-656.10967

512.10967

For this test, we get the p-value as 0.80 which is greater than the given level of significance or alpha value 0.05, so we do not reject the null hypothesis that the average monthly expenditure for the male and female is same. There is sufficient evidence to conclude that the average monthly expenditure for the male and female is same.

The box plots for the monthly expenditure for the persons with different education levels are given as below:

From these box plots, it is observed that there is significant difference in the average monthly expenditure for the persons with different education levels.

The descriptive statistics for the monthly expenditure for the persons with different education levels is given as below:

Descriptive Statistics

Monthly expenditure in AU$

N

Mean

Std. Deviation

Minimum

Maximum

High School/Under-graduate

15

3475.8000

656.47328

2718.00

4768.00

Graduate

16

4660.6875

440.09419

4154.00

5572.00

Post-graduate

19

5468.4737

519.70583

4788.00

6536.00

Total

50

4612.1800

980.83593

2718.00

6536.00

Now, we have to check the claim whether there is any significant difference in the average monthly expenditure for the persons with different levels of education or not. For checking this claim or hypothesis we have to use ANOVA which is given as below:

ANOVA

Monthly expenditure in AU$

Sum of Squares

df

Mean Square

F

Sig.

Between Groups

3.334E7

2

1.667E7

56.773

.000

Within Groups

1.380E7

47

293624.225

Total

4.714E7

49

For this ANOVA we get the p-value as 0.00 which is less than the given level of significance or alpha value 0.05. So, we reject the null hypothesis that there is no any significant difference between the average monthly expenditure in the persons with different education levels. There is sufficient evidence to conclude that the average expenditure of the persons with different education level is different.

Now, we want to check one more hypothesis or claim whether the gender of the person and education of the person is independent from each other or not. For checking this hypothesis or claim we have to use the Chi square test for independence of two categorical variables. Here, we have to check whether two categorical variables gender and education are independent from each other or not. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: The two categorical variables gender and education are independent from each other.

Alternative hypothesis: Ha: The two categorical variables gender and education are not independent from each other.

We assume the 5% level of significance for this test.

The test statistic formula for this test is given as below:

Chi square = ∑[(O – E)^2/E]

Where O is the observed frequencies and E is the expected frequencies.

The expected frequency E is calculated as below:

E = Row total * column total / Grand total

The observed frequency table, expected frequency table and results for this test are summarized as below:

Observed Frequencies

Education

Gender

Under Graduate

Graduate

Post Graduate

Total

Male

8

10

10

28

Female

7

6

9

22

Total

15

16

19

50

Expected Frequencies

Education

Gender

Under Graduate

Graduate

Post Graduate

Total

Male

8.4

8.96

10.64

28

Female

6.6

7.04

8.36

22

Total

15

16

19

50

Data

Level of Significance

0.05

Number of Rows

2

Number of Columns

3

Degrees of Freedom

2

Results

Critical Value

5.991464547

Chi-Square Test Statistic

0.405132149

p-Value

0.816632522

Do not reject the null hypothesis

For the test, we get the p-value greater than the alpha value, so we do not reject the null hypothesis that the two categorical variables gender and education are independent from each other.

Cite This Work

To export a reference to this article please select a referencing stye below:

My Assignment Help. (2021). Statistical Analysis For Categorical And Quantitative Variables - Essay.. Retrieved from https://myassignmenthelp.com/free-samples/bus708-instruction-to-do-data-analysis-and-statistical/categorical-variable-and-a-quantitative-variable.html.

"Statistical Analysis For Categorical And Quantitative Variables - Essay.." My Assignment Help, 2021, https://myassignmenthelp.com/free-samples/bus708-instruction-to-do-data-analysis-and-statistical/categorical-variable-and-a-quantitative-variable.html.

My Assignment Help (2021) Statistical Analysis For Categorical And Quantitative Variables - Essay. [Online]. Available from: https://myassignmenthelp.com/free-samples/bus708-instruction-to-do-data-analysis-and-statistical/categorical-variable-and-a-quantitative-variable.html
[Accessed 22 February 2024].

My Assignment Help. 'Statistical Analysis For Categorical And Quantitative Variables - Essay.' (My Assignment Help, 2021) <https://myassignmenthelp.com/free-samples/bus708-instruction-to-do-data-analysis-and-statistical/categorical-variable-and-a-quantitative-variable.html> accessed 22 February 2024.

My Assignment Help. Statistical Analysis For Categorical And Quantitative Variables - Essay. [Internet]. My Assignment Help. 2021 [cited 22 February 2024]. Available from: https://myassignmenthelp.com/free-samples/bus708-instruction-to-do-data-analysis-and-statistical/categorical-variable-and-a-quantitative-variable.html.

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