Parent’s Income of Public Higher Education College Student

Introduction 

The level of income is an important indicator that can be used to understand the economic status of people. The level of income influences the type and level of education that parents can afford to pay for their children. Investing parents’ income is a step towards understanding the question of the affordability of higher education and can be constructively used to improve government education strategy. This study attempts to study the parents’ income for a group of higher education college students with a view of testing whether the average income is more or less than $40,000. 

Hypothesis 

Null hypothesis, H0: the average parent’s income of public higher education college student is equal to $40,000 ( 

Alternative hypothesis, Ha: the average parent’s income of public higher education college student is NOT equal to $40,000 ( 

Data 

The data was collected through a survey conducted in the college. Stratified sampling method was used where every second higher education college student who approached the college gate was requested to participate in the study. A student who confirmed participation was requested to provide an estimate of their parents’ average annual income. Before data collection, the participants were adequately briefed to ensure that they understood the nature of the study. Participants were also informed about the confidentiality of the data and assured that the data collected would only be used in the study. The participants were not asked to provide personal details such as name, ID number, admission numbers or name of parent to ensure that the data was anonymous. 

Summary Statistics

Table 1 : Descriptive statistics for salary data 

Salary
Mean	42671.4
Median	41822.5
Standard Deviation	4176.54
Range	19865
Min	36567
Max	56432
Q1	40002
Q3	43578
IQ	3576

  The interquartile range estimates the spread of data between the 75 th and 25 th percentile (from the median). The interquartile range explains the spread of the 50% data that is located in the middle after the data is arranged from minimum to maximum. The interquartile range is $3,576 indicating the reduced spread of the public college student income. The standard deviation estimates the spread of the data from the mean. The standard deviation, $ 4,176.54 shows that the income is more spread from the mean as compared to the spread from the median. Both the mean and median estimate the center of the data and the appropriateness is dependent on whether the data is skewed or not. For skewed data, the median is a better measure of central tendency as compared to the mean which is influenced by outliers. 

We can estimate the lower and upper fence to establish whether there are outliers within the data. The fences represent the cutoff points that contain usable data values. The formulas for calculating the lower and upper fence are; 

Lower fence= Q1 – (IQ *1.5) 

Upper fence = Q3 + (IQ *1.5) 

Lower fence = 40002 – (1.5* 3576 ) = 34638 

Upper fence = 43578 + (1.5 * 3576 ) = 48942 

There are no outliers to the left because the lower fence is lower than the minimum value. There are however two outliers that are above the upper fence on the right side. The outliers influence the mean and the standard deviation hence reducing their appropriateness as measures of the center and spread respectively. 

Graphs 

Figure 1 : Box plot for salary data 

The box plot indicates that the data has a tail on the right-hand side and is therefore positively skewed or skewed to the right. This is also proved by a mean that is greater than the median and implies that the median is a better measure of the center while interquartile range is a better measure of the spread. 

Figure 2 : Histogram for salary data 

The histogram also shows the existence of a tail to the right of the data which means that the data is positively skewed. 

Statistical Inference Analysis 

Null hypothesis: the average parent’s income of public higher education college student is equal to $40,000 ( 

Alternative hypothesis: the average parent’s income of public higher education college student is NOT equal to $40,000 ( 

Observed mean = $42, 671.425 

Hypothesize mean = $40,000 

Standard deviation = 4176.54 

Sample size =40 

Critical t-value = 

=  = 4.045 

Rejection region 

Using 39 as the number of degrees of freedom and assuming a 0.05 level of significance the critical value is 2.023. Since the test is two tail, the rejection region is 

Using the rejection region principle, we reject the null hypothesis since 4.045 > 2.023. 

The associated p-value is 0.0002, which is significantly lower than the level of significance, 0.05. This means that there exists sufficient statistical evidence to reject the null hypothesis and conclude that the average parent’s income of public higher education college student is more than $40,000. 

Suggestions 

Use of the stratified method of sampling does not provide an equal chance for all public higher education college student to take part in the study. Use of an online survey sent to all higher education college students would provide an equal chance for all college students who wish to take part in the study and as well help to increase the sample size and thus the reliability of the study results. 

Conclusion 

In conclusion, the sample median income for parents is $ 41,822.5 while the interquartile range is $ 3576. This indicates that the salary is moderately spread from the median meaning that no parent earn incomes that are significantly higher or lower than the median. There however exist isolated cases of outliers in cases where parents’ income is higher than the upper fence. The statistical evidence indicates that parent’s income of public higher education college student is above $40,000. This indicates that higher education may not be affordable for parents with income less than $40,000. 

Appendix

Table 2 : Data obtained from 40 higher college students who were interviewed during the survey. 

Respondents	Parent salary
1	43200
2	43150
3	41150
4	53130
5	40045
6	51336
7	45621
8	38454
9	46342
10	42512
11	39505
12	40075
13	42102
14	41231
15	40145
16	38543
17	38672
18	39649
19	39945
20	42134
21	41203
22	45102
23	43632
24	44305
25	43202
26	42334
27	51024
28	46452
29	41543
30	39562
31	38908
32	56432
33	40021
34	40563
35	39895
36	36567
37	41078
38	42369
39	42164
40	43560