Question

The 95% confidence interval for the population mean was calculated based on a random sample with sample size of n=31 as (50 to 60). Calculate the outcome of a 2 sided alpha=0.05 test based on the null hypothesis of H0: mean=55, and determine if:

A.We would reject the null hypothesis.

B. We would accept the null hypothesis.

C. We woudl fail to reject the null hypothesis.

D. Not enough information to decide.

Answer 1

The answer is

We would fail to reject the null hypothesis

Reason:

Since the 95% confidence interval for population mean based on sample contain the hypothesised mean ( 55)

That means the our test statistic is in acceptance region with alpha = 0.05

So with (1-0.05)% that is 95% confidence we can say that there is no significant difference between the observed value and hypothesised value

If the 95% confidence interval doesn’t contain the hypothesised value, test statistic is in rejection region , we reject the null hypothesis