Question

A researcher wants to find out if there is a significant difference between men and women in the average number of tattoos that a person has. After doing the statistical analysis, the researcher finds that the p-value is 0.003. If the chosen significance level is 0.05 (5%), which of the following statements is the best interpretation of this p-value?A. The results are statistically significant.B. The results are not statistically significant.

C. The magnitude of a p-value has no impact on statistical significance.

Answer 1

The correct option is (A).

Explanation:

The p-value is well-defined as per the probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was the truly observed value of the test statistic.

A small p-value (typically p < 0.05) specifies strong evidence against the null hypothesis (H₀), so the null hypothesis is rejected. A p-value less than 0.05 is considered as statistically significant.

A large p-value (p > 0.05) specifies fragile proof against the H₀, so the null hypothesis is failed to be rejected.

In this case the p-value of the test is,

p-value = 0.003

And the significance level of the test was,

α = 0.05.

p-value = 0.003 < α = 0.05.

The p-value less than the significance level of the test.

Thus, the results are statistically significant.

The correct option is (A).