Question

what does failing to reject the null hypothesis imply?
a. there isnt sufficient evidence to support the alternative hypothesis
b. there was a calculation error in determining the p - value
c. the alternative hypothesis is definitely false
d. the null hypothesis is proven true beyond a doubt

Explanation:

In hypothesis testing, failing to reject the null hypothesis means that the data does not provide enough evidence to support the alternative hypothesis. It does not mean the null hypothesis is proven true (as there could be Type - II error), nor does it mean the alternative hypothesis is definitely false. Also, it has no relation to calculation error in p - value (unless specifically stated).

Answer:

A. There isn't sufficient evidence to support the alternative hypothesis