## Background

In today’s world, human resources is a significant factor to determine the strength of a country or a district. And university education is considered a core part to develop the human resource. When talking about a university, the tuition fee will be the topic people concern about.

As we know, the tuition fee of all Hong Kong universities is HK$ 42,100 for local students, which is different from the situation in Mainland China. First, tuition fee always varies in different universities, even in different majors of the same university.

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Second, except for some art academies, the range of tuition fees is from RMB 3,000 to 8,000 per year, which seems much less than that in Hong Kong. Nevertheless, it is often reported in the news that some students from poor families dropped out of school because of the economic pressure.

Even some families in rural areas sell their houses or cattle to support their children to get access to university education. How do these differences come about? Do universities with higher ranking charge higher tuition fees? In respect to different economic conditions, is the tuition fee reasonable in certain countries or areas.

## Objectives

In this report, we aim to gain an insight into tuition fees of universities in Mainland China through conducting statistical analysis of 100 universities sampled from the top 600, using per capita GDP as the base to evaluate tuition fees.

## Methodology

Sources The data is collected from the Internet so does the news about tuition fees. The main information is a list of the top 600 universities in Mainland China and a list of per capita GDP of every province in mainland China. Sampling Method The sample size is determined to be 100 and the systematic sampling method is chosen. According to the method, 600 parameters are divided into 100 groups. Therefore, every group contains 6 universities (k=N/n=600/100=6). In the first group, the 2nd item is selected at random.

Then, we select the remaining 99 items by taking every 2nd item in the remaining 99 groups thereafter. Data Processing of Tuition Fee Most of our sample universities are comprehensive universities and the tuition fee varies from major to major. For convenience, data is selected based on the following two steps:

- Eliminate extreme value
- Select the median tuition fee of different majors as the representative

For example, the following is the tuition fee charged for different majors at the University of International Relations (UIR).

As a result, we selected RMB5500 as the representative tuition charged by UIR. Techniques We use simple linear regression model and correlation, one sample testing, and two sample testing to analyze the tuition fee of universities in Mainland China. Excel is made good use of to construct diagrams like histogram and polygon, making the analysis more visualized.

## Analysis

### Relationship between the Tuition Fee and the Ranking ]

We use the Scatter Diagram to examine possible relationships between the Ranking and Tuition fees of Universities in Mainland China. As the figure shows, the tuition fee is measured on the vertical axis and the ranking from 1 to 100 is measured on the horizontal axis.

The scatter diagram shows that there is a slight negative slope, which implies that there is no strong relationship between these two numerical variables. Thus, we can get a rough idea of the weak relationship between the tuition fee and the ranking.

Besides, in order to measure the relationship, regression analysis is performed by excel. The R2, coefficient of determinations, is 0. 034467, which proves the weak relationship between the two factors. In conclusion, from the appearance of the scatter diagram and the result of the regression analysis above, tuition fees and ranking have no direct relationship.

### Relationship between the Tuition Fee and the World Standard

A frequency distribution is here made for these 100 universities, according to the empirical rule, we find out that 68% of our sample data is within? ±1?.

What’s more, through the frequency polygon, it’s obvious that our sample is almost normally distributed. According to the world standard, the tuition fee should equal to or smaller than 20% of the per capita GDP. Therefore, we have conducted a hypothesis testing for this claim to see whether China is in accordance with the standard. Then, the null hypothesis, H0 is that the tuition fee is no more than 20 percent of the per capita GDP, which is RMB 3648 (2007 per capita GDP = USD2280, 1USD: 1RMB=8:1, per capita GDP of 2007= RMB 18240). On the other hand, the alternative hypothesis, H1 is that the tuition fee should be more than 20% of the per capita GDP. And the level of significance? = 0. 0 is chosen for this test. Thus, it is a one-tail test with? unknown.

Our finding can explain the fact that there are still many families in China who can not afford the college fee and no wonder that every year a lot of students are forced to quit their colleges. This education problem in Mainland China is a hot topic now. To make a further comparison, we also study the case in Hong Kong to get an insight into the situation. The following data is found. |Per capita GDP in Hong Kong of 2007 |232800 HKD/Year | |College tuition fee in Hong Kong |42100 HKD/Year | After the calculation, it is found that the college tuition fee in Hong Kong only takes up 18. 1% (42100 HKD/ 232800 HKD) of per capita GDP.

We surprisingly found that even though the college tuition fee of Hong Kong is almost 10 times higher than that of Mainland China, if we consider per capita GDP as well, it is not the case at all. In fact, the tuition fee in Mainland China is relatively higher than that of Hong Kong.

## Provinces in Accordance with the Hypothesis

As we know, inequality in wealth is a big problem in China, especially for the region difference between the eastern provinces and the others. It’s necessary for us to find out which province is in accordance with the hypothesis. Firstly, we need to find the required per capita GDP to separate the qualified and unqualified ones. In proportion to the claim, the tuition fee (mean= RMB 4500. ) should take up 20% of the per capita GDP, so the required GDP would be RMB 22504. As the table (Per Capita GDP for Each Province in Mainland China) illustrates, those provinces ranking the top 10 are in line with the claim. It is apparent that almost all these 10 provinces are located in the eastern part of China. In order to find out whether there is a difference in tuition fees between the east and the west, two-sample testing is performed to compare the level of tuition fees between the eastern and non-eastern parts of China.

According to the official classification of the Chinese government, the eastern part includes Heilongjiang, Jilin, Liaoning, Beijing, Tianjin, Shandong, Jiangsu, Shanghai, Zhejiang, Fujian, Guangdong, and Hainan. Then the remaining provinces belong to the non-eastern part. We suppose H null is that the mean of the tuition fee in the east of China is not higher than that of the western part. So H1 is our hypothesis. [pic] There are 65 universities which are located in the east and 35 in the west among our 100 sample universities, that is, and d. f. =98. Do we choose the level of significance? =0. 10, thus critical value is found in the t- table which is 1. 290.

Figure 3. 2 testing a hypothesis about mean (sigma unknown) at 0. 1level of significance with98degrees of freedom After the calculation of the mean and pooled standard deviation, t statistic is come out to be 1. 927 which is much higher than the critical value 1. 290, so obviously, H0 should be rejected and we have 90% confidence to claim that the tuition fee of universities in the east part of China is higher than that in the west. We can draw from the calculation that the tuition fee is not a heavy burden for all regions in China. Because of the inequality in wealth, the average tuition fee can be viewed differently from different perspectives.

However, the majority of the families still can not afford the expensive fee.

## Conclusion

Using correlation and regression to test the relationship between college tuition fees and the ranking, it is found that these two variables are not directly related. As for whether the tuition fee is cheap or not, we use hypothesis testing and the generally accepted standard that the tuition fee should equal to or less than 20% of the GDP per capita. The result is somewhat astonishing that the tuition fee is relatively high since the average statistic is above the standard. On the contrary, the tuition fee of Hong Kong, which seems to be quite high, is relatively low according to our testing technique.

In addition, it turns out to be that 10 provinces or cities are well-suited to the standard, and most of them locate in the eastern part of China. From the above analysis, we come up with a thunderclap that the college tuition fee in China is in fact relatively high compared with other regions around the globe, which is opposed to what it seems to be. Maybe that is why many Chinese families claim that they cannot afford the tuition fee. This is an education problem that the government should face. Therefore, more education loans and scholarships are encouraged to help needy students complete their university education. What’s more, all these findings are an indicator of the serious inequality in wealth in China.

Thus, students from rural areas and the western part of China should be provided with extra education financial aid.

## Limitations

- The population in our study is the tuition fee charged by the top 600 universities in Mainland China. The tuition fee for art academies is excluded because it is extremely high which can be perceived as an outlier. By excluding them we aim to avoid bias in study results. Thus, the coverage of the study is limited.
- As demonstrated in the part of the methodology, we select the median tuition fee of different majors as the representative of the university. By this means our sample data is a part reflection of the real tuition fee of the sample universities.
- All data we use in the study is secondary data searched from the Internet. The data may not be accurate due to the complexity of the real situation.