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## Hypothesis Testing

## Paired Sample t-test with R Studio

This project analyzes whether tutorials are helping students to improve understanding in their study.

The hypothesis test is set as follows:

H0:μΔ=0

HA:μΔ≠0

The data used on this project is collected from a school and not available for public.

The hypothesis test is set as follows:

H0:μΔ=0

HA:μΔ≠0

The data used on this project is collected from a school and not available for public.

**Descriptive Statistics**

First, let's check the statistic summary of the students before and after tutorial.

From the descriptive statistic result, we can see that before tutorial, the average score is 35.82 and after tutorial, the average score increased to 41.17. Tutorial seems to be helpful to improve the students' score.

We will perform Paired-sample t-test (one-sample t-test) for the difference between before and after tutorial to investigate whether there is any significant different.

We will perform Paired-sample t-test (one-sample t-test) for the difference between before and after tutorial to investigate whether there is any significant different.

Upon performing boxplot, there seems to be an outlier in after tutorial data. However, the outlier is real and therefore is needed. Several visualizations such as QQ plot, Matplot, and Granova will be performed to check the improvement of the score.

**Conclusion**

A paired sample t-test was used to test for a significant mean difference between the scores of students before and after tutorial. The mean difference following tutorial was found to be 5.350, SD = 10.038.

Visual inspection of the Q-Q plot measuring the difference suggested that the data were approximately normally distributed. The paired-sample t-test found a statistically significant mean difference between scores before and after tutorial with t(df=1289) = 19.144, p < 0.001, 95% [4.80, 5.90]. The t critical value is ± 1.962.

Scores were found to be significantly improved after tutorial.