Which of the following p-values would signify that a sample correlation…

Concept

In hypothesis testing, the significance level α is the maximum probability of a Type I error that the researcher accepts before examining the data.

The p-value measures how unusual the observed result, or a more extreme result, would be if the null hypothesis were true. A result is statistically significant when p < α.

Application

1. Here, α = 1% = 0.01.

2. Compare each offered p-value with 0.01: only 0.005 is smaller than 0.01.

3. Therefore, the sample correlation coefficient is significant at the 1% level for p = 0.005.

Contrast and cross-check

• 0.02 represents 2%, which is above the 1% threshold.

• 0.99 represents 99%, which is far above the 1% threshold.

• 0.95 represents 95%, which is also far above the 1% threshold.

Cross-check: 0.005 ÷ 0.01 = 0.5 < 1, confirming that 0.005 lies below α. Hence, the required p-value is 0.005.