The correlation matrix above shows that there is the strong positive correlation between listening and reading.When t-test is carried on the group with fewer samples, it is observed that the p-value is less than 0.05 and this means that the data is valid or statistically significant. The t calculated is seen to be greater than t critical. This means that the null hypothesis is rejected and we conclude that there is a statistically significant difference between the mean score of listening and reading when doing math test. In reference to the correlation matrix which showed that there was a strong relationship between the two, it can be suggested that this relationship does exist because there is the statistical difference between the two variables.When t-test was undertaken on the group with 34 degrees of freedom it is observed that the p-value is slightly higher than 0.05 and this makes it hard to make a conclusive statement on the data validity or on the hypothesis. Therefore, this implies that a bigger sample size that is greater than 30 is not relevant when t-test is used. In this case, this sample size can’t be used in either rejecting or accepting the hypothesis. In conclusion, it is clearly evident that there is a strong positive correlation between a person’s IELTS scores in listening and reading when doing the math. In addition, it was shown that listening is directly proportional to reading and it was indicated by the regression line. When the hypothesis was tested, it was clear that there is a statistically significant difference between a person’s IELTS means scores in listening and reading when doing the math. This was correct when a group with the fewer sample was used, but it was not the case for the group with a larger sample size greater than 30.In this case, the p-value was recorded to be almost the same as 0.05 and it was concluded that the data was not statistically significant to make a conclusive statement on the hypothesis.
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