Question

If you compute a 95% confidence interval for a sample and conclude that it doesn't provide sufficient evidence to prove a hypothesis--and then compute a 90% confidence interval from the same sample data, would there still be insufficient evidence or would your answer change?

Answer 1

If we compute a 95% confidence interval for a sample and conclude that it doesn't provide sufficient evidence to prove a hypothesis that means the desired or expected population parameter is in the confidence interval hence we were not able to reject the null hypothesis.

So, if we compute the 90% confidence interval that will be narrower than a 95% confidence interval because the Z-score decreases as the confidence level decreases, and the Z score is directly proportional to the confidence interval.

The Confidence interval is calculated as:

CI = M +/- Zc* SE

Where M is the sample mean or could be sample proportion, SE is the standard error.

Hence there may be a possibility that the desired population parameter will not be in the confidence interval hence we can have sufficient evidence and hence answer can change.

Note: Feel free to ask if the query remains.