Confidence Interval for Population Proportions

A study of teenage suicide included a sample of boys and girls between the ages of 12 and 16 years selected scientifically from admission records to a private psychiatric hospital (Daniel, 1999) . Let population 1 be the population of boys and population 2 be the population of girls. 

The level of confidence is c = 0.95, so the critical value is z α/2 = z 0.05/2 = z 0.025 = 1.96. 

Thus, the 95% confidence interval for the difference between the two population proportions ranges from -0.018901 to -0.017645.

The p value, also known as calculated probability, is the level of marginal significance within a statistical hypothesis test that represents the probability of the occurrence of a given event ("P-Value," n.d.) . Statistical probabilities such as the p-value range from 0 (no chance) to 1 (absolute certainty). P-values are calculated using statistical software or p-value tables. Since various studies use different significance levels for their research results, it becomes difficult for the reader to predict the outcomes of those particular studies. Due to this inconvenience, the p-value method towards hypothesis testing is used to allow the reader to check the validity of the stated outcomes of the study in order to strengthen the research findings. 

An article in a scientific journal criticizes the p-value and states it is being used in scientific research to support unrepeatable results . The American Statistical Association (ASA) recommends that the final conclusions of any research study should not be based primarily upon the p-values. A p-value of 0.05, for example, does not suggest a 95% probability of the hypothesis being true but a 5% chance of the outcomes of the study being reproducible. Critics of the p-value method used for scientific research have suggested various control measures and one of them includes banning such research publications from scientific journals (Baker, 2016) . 

Solving a Hypothesis Testing Problem Using the P-Value Method 

An investor claims her portfolio’s performance is equivalent to the Standard & Poor (S&P) 500 index. By conducting a two-tailed test, if the null hypothesis states that the investor’s revenue returns are equivalent to the S & P standards and if the p-value is calculated to be greater than 0.05, then the null hypothesis is proved. Consequently, the alternative hypothesis which declares the revenue returns to be unequal to the S&P standards and if the p-value is calculated to be less than 0.05, then the alternative hypothesis is proved ("P-Value," n.d.) . In this way, calculated probabilities are used to test the statistical significance of hypotheses statements. 

References

Daniel, W. W. (1999). Confidence Interval for the Difference of Two Population Proportions. Biostatistics: A Foundation for Analysis in the Health Sciences. Retrieved from https://www.kean.edu/~fosborne/bstat/06d2pop.html 

P-Value. (n. d). In Investopedia. Retrieved from https://www.investopedia.com/terms/p/p-value.asp 

Baker, M. (2016). Statisticians issue warning over misuse of P values. Nature . 531 (7593). Retrieved from https://www.nature.com/news/statisticians-issue-warning-over-misuse-of-p-values-1.19503