A researcher obtains the following p-values for sample correlation coefficients of different samples. Which of these can be considered significant at 1% level of significance?

(A) 0.004

(B) 0.99

(C) 0.995

(D) 0.001

(E) 0.1

Choose the correct answer from the options given below:

The correct answer is B & C only.

Here is the step-by-step explanation of why this option is correct:

1. Understanding the Level of Significance and Confidence Level
In statistical hypothesis testing, the level of significance (denoted by α) represents the probability of rejecting the null hypothesis when it is actually true. A 1% level of significance corresponds to a confidence level of 99%.

Mathematically, we can express the relationship between the level of significance and the confidence level as follows:
$$\text{Confidence Level}=1-\alpha$$
Given that the level of significance is 1% (or 0.01):
$$\text{Confidence Level}=1-0.01=0.99\text{(or 99\%)}$$

2. Comparing the Given Values to the Threshold
To determine which values are significant at the 1% level of significance, we identify the values that meet or exceed the 99% confidence threshold of 0.99:

• (A) 0.004: Since 0.004 is less than 0.99, it does not meet the threshold.
• (B) 0.99: Since 0.99 is equal to 0.99, it meets the threshold.
• (C) 0.995: Since 0.995 is greater than 0.99, it meets the threshold.
• (D) 0.001: Since 0.001 is less than 0.99, it does not meet the threshold.
• (E) 0.1: Since 0.1 is less than 0.99, it does not meet the threshold.

3. Conclusion
Only the values under (B) and (C) satisfy the condition of meeting or exceeding the 0.99 (99%) confidence level associated with a 1% level of significance. Therefore, B & C only can be considered significant.