# Practical Application Paper: Inferential Statistics

The faculty wants to know whether the new style of teaching is more helpful to the 9th and 12th grade students than the old teaching style. To confirm whether the new style is indeed better, the faculty conducted a Studentâ€™s T-test on the average scores of the student. The null hypothesis is the average score of the students is the same after the new teaching style is applied. The alternative hypothesis is that the average score of the students is higher after the new teaching style is applied.

A 50-item test is given to a sample of 50 9th and 12th grade students. The scores were recorded and gave an average score of 29. 28. Then, the faculty used the new teaching strategy to the sample students for a week. After a week, the faculty gave the same test for the students and the result was 44. 18. The average scores of the students, before and after the new teaching style is applied is, were compared. The average score is tested at 0. 05 significance level. The decision is to reject the null hypothesis if the probability is less than 0.05.

Since the computed probability is less than 0. 05 which is 9. 76717×10-33, the null hypothesis is rejected. The faculty is 95% confident that the average score of the students is higher after the new teaching style is applied. The faculty is convinced that the new teaching style is more helpful to 9th and 12th grade students. Inferential tests such as T-test are used in order to know something about the population given a sample taken from the population itself.

For example, if a parameter such as the mean is unknown for the population, one uses statistic from the sample in order to understand the population. The inferential tests always use probability in order to confidently assume something from the population. This probability is known as the significance level. The probability of the sample statistic is compared to the significance level. Then from the comparison, a conclusion is obtained (Trochim, 2006).

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