A 95% confidence interval for a population mean is (28,35). can you reject the null hypothesis?

Question

the significance level is at 5%. why do we reject or except the null hypothesis? help on how to do this would be greatly appreciative.

Answer 1

the confidence interval (28, 35) tells us the possible plausible values for the null mean.  If you have a null mean that is not covered by the confidence interval then you will find that running the corresponding hypothesis test will reject the null hypothesis.    On the other hand, if your null hypothesis is contained with in this interval, then you will find the corresponding hypothesis test will fail to reject the null.

Answer 2

considering the standard deviation is 35, thats a pretty big deviation.

if you were to be 95% confident, you would have to go out 2 standard deviations which would be insignificant which would mean that the sample mean could be from -42 to 98 which is too large of an area to be precise about a population mean.

reject the null hypotheses as 95% confidence interval.