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Forthe paper to determine if there is significant departure from theaverage temperature for the date given in a particular location isthe standard deviation and the standard error. Standard error is usedto measure the statistical accuracy of an estimate(Samuels, Witmer &amp Schaffner, 2012).The standard deviation helps the researcher to understand how far thetest static deviates from the group or larger sample as a whole(Loughran &amp McDonald, 2014). Further, the standard deviationenables the researcher to construct the t-statistic, which is used tocompare the t-critical from the t-statistic table.

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Usually,it is admitted within research that the use of the same test for preand post study is critical. The criticality in most cases is linkedto the need of having a study that is integral in nature. A studybeing of integrity in this sense means that the study has a decreasedstandard error (Bluman, Cheviakov &amp Anco, 2010). For sure,having a decrease in the standard errors requires that there beconsistent means by having same testing processes at all thedifferent phases of the study. To deliver according to the study, itis important that the researcher indeed identify the variables in thestudy. Identification of variables means having distinction betweenindependent and the dependent variables (Williams, 2011).

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Often,the critical value is used against the test statistic to determinewhether to reject or fail to reject the null hypothesis (Razali &ampWah, 2011). From the study, it appears that the larger the studysample, the lower the critical value. With low critical value, thechance to reject the null hypothesis is reducing. Therefore, with alarger sample, indeed there is likely to be a connection establishedbetween the 8-week program and the self-esteem.

References

Bluman,G. W., Cheviakov, A. F., &amp Anco, S. C. (2010).&nbspApplicationsof symmetry methods to partial differential equations&nbsp(Vol.168, pp. xx+-398). New York: Springer.

Gravetter,F. J., &amp Wallnau, L. B. (2016).&nbspStatisticsfor the behavioral sciences.Cengage Learning.

Loughran,T., &amp McDonald, B. (2014). Measuring readability in financialdisclosures.&nbspTheJournal of Finance,&nbsp69(4),1643-1671.

Razali,N. M., &amp Wah, Y. B. (2011). Power comparisons of shapiro-wilk,kolmogorov-smirnov, lilliefors and anderson-darling tests.&nbspJournalof statistical modeling and analytics,&nbsp2(1),21-33.

Samuels,M. L., Witmer, J. A., &amp Schaffner, A. (2012).&nbspStatisticsfor the life sciences.Pearson education.

Williams,C. (2011). Research methods.&nbspJournalof Business &amp Economics Research (JBER),&nbsp5(3).