# Using Statistical Test Method to Establish a Decision Model of Performance Evaluation Matrix
## 6 Conclusions  
According to the viewpoints of [PERSON], [PERSON], and [PERSON] [14], we proposed standardized and significant indices of importance and satisfaction on the premise that satisfaction and importance were assigned by Beta in this paper, and the values of these two indices were both between 0 and 1. Next, we set the satisfaction index as \(x\)-axis and the importance index as \(y\)-axis to form a performance evaluation matrix. In order not to lose generality, we assumed that the digital learning service items provided by the teaching APP in this paper had a total of \(q\) service items, so there were \(q\) satisfaction indices and \(q\) importance indices in total. First, in this paper, we determined the unbiased estimators of the satisfaction index and the importance index for all service items since the indices had unknown parameters. Second, we used the average value \(\theta_{0}^{5}\) of all satisfaction indices as the testing standard in accordance with the spirit of continuous improvement on the comprehensive product management as well as adopted the statistical one-tailed test to determine the critical value \(C_{0}^{5}\). Third, we established testing rules to facilitate the management to procure the service items that need to be improved. At the same time, the average value \(\theta_{0}^{I}\) of all the importance indices was adopted as the testing standard, and the ranking of all service items that need to improve was determined by the statistical one-tailed test. Next, the above two statistical testing rules were applied as the basis of defining the PEM evaluation blocks and establishing the PEM evaluation rules. Obviously, since the method in this paper was established via statistical tests, the risk of wrong judgment caused by sampling error can be diminished. After the task of improvement was completed, we employed the statistical two-tailed test to verify whether the satisfaction of all key service items that need to make improvements was leveled up. Finally, a case study of the computer-assisted language learning system (CALL System) was used to explain the application of the abovementioned statistical testing rules. As noted above, most studies just identify critical qualities (CTQs) that need improvement, without discussing processing rules in resource-limited settings, and without confirmation of improvement. The method of this paper just makes up for the gap in similar research. This paper adopts the one-tailed statistical hypothesis testing method of satisfaction index, which can help the industry to detect the CTQ service items that need to be improved and determine the order of improvement with a low risk of misjudgment. Finally, the two-tailed statistical hypothesis testing method is used to assist the industry to confirm its improvement effect. In addition, the digital learning effect evaluation and improvement model of the teaching APP constructed in this paper will contribute to attracting more users to apply the teaching APP to achieve the effectiveness of digital learning. The APP enables more students to avoid the inconvenience of going out and obtain good learning outcomes at home. Not only can it alleviate the problem of traffic congestion, but it can also achieve the effect of energy saving and carbon reduction by decreasing the need of going out. Clearly, this paper refers to the literature, closely examines the needs of the customers, and assumes that the distribution of customer satisfaction and importance lies with Beta distribution since Beta distribution belongs to continuous probability distribution; however, data would have to be collected from the highest score of 100 and the lowest score of 0 and then divided by 100 to produce a value between 0 and 1. In addition, the statistical test must be conducted by the Central Limit Theorem. These are the limitations of this study. Therefore, future research can focus on the data collection method of the Beta distribution, and explore the fitting quantity of sample size in the application of the Central Limit Theorem.