Question

In a right-tailed test, the p-value is calculated as p(z > test statistics). The p-value is generally compared with 5. What is the purpose of comparing the p-value with 5?

1) To determine the statistical significance of the test
2) To determine the direction of the test
3) To determine the effect size of the test
4) To determine the power of the test

Answer 1

Comparing the p-value with 0.05 in a right-tailed test is done to determine the statistical significance of the test. A p-value less than 0.05 typically leads to rejection of the null hypothesis, indicating the observed effect is probably not due to chance.

Step-by-step explanation:

In a right-tailed test, the purpose of comparing the p-value with 5, which actually means 0.05 or 5%, is to determine the statistical significance of the test. When we say a result is statistically significant, we mean that the evidence in the data is strong enough to suggest that the effect observed (or the difference from the null hypothesis) is not due to random chance.

The null hypothesis is rejected if the p-value is less than the level of significance, α, which is commonly set at 0.05 (5%). The alternative hypothesis, Ha, determines whether the test is left, right, or two-tailed. If Ha suggests that the parameter of interest is greater than some value, then a right-tailed test is appropriate.

A lower p-value, such as 0.001, gives more confidence in rejecting the null hypothesis compared to a p-value that is just below the significance level, such as 0.049, when α is 0.05. Conversely, higher p-values, like 0.4, suggest there is not enough evidence to reject the null hypothesis and it is more likely that any observed effect could have happened by chance.