Hypothesis testing is one of the basic concepts in inferential statistics, and it is usually run with the aim of determining whether or not a specific claim is true or on, given a population. As part of the test, it can be conducted to show whether the mean of a sample is significantly greater or less than the mean of the considered population or if its lower or higher than the population mean (Kruschke & Liddell, 2018). Therefore, the purpose of this assignment is to answer questions on hypothesis testing.

A one-tailed test is a case where the critical area of distribution is one-sided so that it is either less than or greater than a particular value but not both (Lakens et al.,2018). An example is a case where a researcher wants to study whether a learner’s class attendance would affect their grades, so a one-tailed hypothesis would be that those with higher attendance will have significantly higher grades compared to those with low attendance. On the other hand, for a two-tailed hypothesis, it will be that a significant difference in the grades between students with low attendance and those with high attendance will occur.

• In a case where a researcher has set alpha at 0.05 for a two-tailed test, there is a range of p-values that would be required to reject the null hypothesis. For instance, the null hypothesis will be rejected if the p-values are less than or equal to the alpha (Ware et al.,2019). So, in this case, any p-value less than or equal to 0.05 leads to a rejection of the null hypothesis.
• In the case where a researcher sets an alpha at 0.05 and analysis from a software program gives a p-value of 0.92, the researcher can not reject the null hypothesis. This is because the value 0.92 is greater than the alpha value, which is 0.05. This means that the null hypothesis is more likely to be true (Ware et al.,2019).
• In the case where a researcher has set alpha at 0.01 and upon analysis using a software program, then he obtains a p-value equal to 0.04, then the research must fail to reject the null hypothesis. The researcher can not reject the null hypothesis since the p-value obtained is greater than the value of alpha. The condition for rejecting the null hypothesis is that the obtained p-value should be less than or equal to alpha (List et al.,2019).

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• In the case of a researcher interested in whether music played during an exam will improve performance, the alpha  is set at 0.05; those who listened to music had a score of 92, while those who took the exam in silence got a score of 82, and the independent t-test is 0.02, the null and alternative hypothesis can be stated as:
• H0: There is no difference between the performances of the student who took the exam listening to music and the student who took the exam in silence
• H1: There is a difference between the performances of the student who took the exam listening to music and the student who took the exam in silence
• This is a directional test because the is an increase and decrease in performance away from the mean. It is evident that there was a decrease of thirteen marks between students who had music on and those who took exams in silence.
• The p-value obtained is 0.02, which is less than the set alpha (0.05); therefore, we reject the null hypothesis. The conclusion is that the results are statistically significant.
• Type 1 error will occur in a case where the null hypothesis is rejected even if it is true (Siedlecki, 2020). Reject the null hypothesis that there is no difference in the performance; however, from the result, there was a difference. The students performed better while listening to music. Type II error occurs when the null hypothesis is accepted even if it is false. For example, accepting that there is a difference in performance and it is false.

### References

Kruschke, J. K., & Liddell, T. M. (2018). The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective. Psychonomic Bulletin & Review25, 178-206. Doi: 10.3758/s13423-016-1221-4

Lakens, D., Scheel, A. M., & Isager, P. M. (2018). Equivalence testing for psychological research: A tutorial. Advances in Methods and Practices in Psychological Science1(2), 259-269. https://doi.org/10.1177/2515245918770963

List, J. A., Shaikh, A. M., & Xu, Y. (2019). Multiple hypothesis testing in experimental economics. Experimental Economics22, 773-793. 10.1007/s10683-018-09597-5

Siedlecki, S. L. (2020). Understanding descriptive research designs and methods. Clinical Nurse Specialist34(1), 8-12. 10.1097/NUR.0000000000000493

Ware, J. H., Mosteller, F., Delgado, F., Donnelly, C., & Ingelfinger, J. A. (2019). P values. In Medical uses of statistics (pp. 181–200). CRC Press. Doi: 10.1201/9780429187445