can someone explain why the confidence interval CANNOT be interpreted as a 95% c

Question

can someone explain why the confidence interval CANNOT be interpreted as a 95% chance that the true difference is between the upper and lower bounds for the confidence interval (i.e., can someone explain why the answer can't be A)?

A 95% confidence interval for the difference between two population proportions p - p2 is (-0.02, 0.14). Based on this interval, which of the following is correct? (A) There is a 95% chance that p1-p2 ls between-0.02 and 0.14. (B) It can be said, with 95% confidence, that there is not a statistically significant difference between the value of p and the value ofp2. (C) It can be said, with 95% confidence, that the value of p1 is between 0.02 and 0.14 less than the value of p (D) It can be said, with 95% confidence, that the value of p1 is between 0.02 and 0.14 more than the value of p2-

Explanation / Answer

If we need to compare the difference in proportions based on confidence interval, we just check whether 0 is included in the given interval or not. If 0 is not included in the interval then that means there is a significant difference between the given proportions and if 0 is included in the interval then that mean there is no significant difference.

Here in this case, the interval (-0.02, 0.14) includes 0 and hence, there is no significant difference.

Option B is correct.

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