# P-value, test statistic, level of significance and critical value

Prepare a three-paragraph discussion of the relationship between p-value, test statistic, level of significance, and critical value. Allot one paragraph for each term. Discuss p-values for two sided and one-sided tests. Provide an example for tests using Z, Student-t, and Chi-squared. Provide equations for each when possible and discuss how these terms help with hypothesis decisions.

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#### Solution Preview

The p-value approach is a recent development in hypothesis testing procedure when it has become much easier to calculate exact probabilities using computer software such as MS Excel, SPSS, SAS, Megastat etc. p-value is the probability of obtaining a value of the test statistic as extreme as the one calculated under the assumption that the null hypothesis is true. If p-value is less than the level of significance, the null hypothesis is rejected, no matter whether it is a left-tailed or right-tailed or two tailed test. Normally, the default level of significance (which is also called the probability of committing a Type I error) is 0.05, and the decision rule in the hypothesis testing process is to reject the null hypothesis if p-value is less than 0.05.

The test statistic is the value calculated using the sample data, namely, the mean, the standard deviation and the sample size. If the test statistic value comes out to be larger than the critical value in a right-tailed test or smaller than the critical value in a left-tailed test, the null hypothesis is rejected. If the absolute value of the test statistic is larger than the critical value in a two-tailed test, the null hypothesis is rejected again.

The level if significance, also called the probability of Type I error, is a fraction or percentage which demarcates the acceptance ...

#### Solution Summary

P-value, test statistic, level of significance and critical value are discussed. Equations are provided to discuss hypothesis decisions.