Question

A 95% confidence interval for a population mean was calculated. The sample mean was found to be 34.5 and the MOE was found to be 4.06 giving us a confidence interval of 34.5±4.06 or equivalently written as 30.44 to 38.56.

(a) For the hypotheses H0:?=30 Ha:??30, would you reject the null hypothesis at the 5% level of significance (i.e. ? = 0.5)? (Type: YES or NO or CANNOT TELL):

(b) For the hypotheses H0:?=41 Ha:??41, would you reject the null hypothesis at the 5% level of significance? (Type: YES or NO or CANNOT TELL):

(c) In general, you reject the null hypothesis if ? is the equivalent confidence interval. (Type: IN or NOT IN)

Answer 1

The confidence interval is (34.5, 38.56)

a) The hypotheses is H0:?=30 Ha:??30

?=30 does not belong to the confidence interval.

so we reject the null hypothesis.

b) The hypotheses H0:?=41 Ha:??41

?=41 does not belong to the confidence interval.

So we reject the null hypothesis.

c) NOT IN

If $\mu$ belongs to the confidence interval we fail to reject the null hypothesis and $\mu$ is not belongs to the confidence interval we reject the null hypothesis.