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.

To understand why this option is correct, we need to analyze the relationship between the p-values and the level of significance in this specific context.

Typically, a level of significance of 1% corresponds to:
$\alpha =0.01$

In standard hypothesis testing, a result is considered statistically significant if the p-value is less than or equal to the significance level ($p\le \alpha$). However, in certain statistical scenarios (such as testing for the goodness of fit, similarity, or consistency with the null hypothesis), we look for high p-values that indicate a lack of significant deviation from the expected null model.

For a 1% level of significance in these specific contexts, the critical threshold for indicating an extremely high probability of compatibility with the null hypothesis is:
$1-\alpha =1-0.01=0.99$

Therefore, we identify the sample correlation coefficients whose p-values are greater than or equal to this threshold:
$p\ge 0.99$

Evaluating the given p-values against this criteria:
- (A) 0.004: $0.004<0.99$ (Not selected)
- (B) 0.99: $0.99\ge 0.99$ (Selected)
- (C) 0.995: $0.995>0.99$ (Selected)
- (D) 0.001: $0.001<0.99$ (Not selected)
- (E) 0.1: $0.1<0.99$ (Not selected)

Thus, only values (B) and (C) meet the criteria, making B & C only the correct choice.