Question

1. what does failing to reject the null hypothesis imply?

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

Explanation:

In hypothesis testing, failing to reject the null hypothesis ($H_0$) does not prove $H_0$ is true. It means that based on the sample data and the chosen significance level, there is not enough evidence to support the alternative hypothesis ($H_1$). Hypothesis testing is about evidence from data, not absolute proof. A non - rejection of $H_0$ could be due to various reasons like a small sample size, high variability in the data, etc., but not because of a calculation error in the p - value (unless specifically shown). Also, we cannot say the alternative hypothesis is definitely false; we just lack evidence to support it.

Answer:

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