Question

2. A 95% confidence interval for ?? − ?? is (-4.5, -0.15). Based upon the data from which the confidence interval was constructed, someone wants to test H0: ?? = ?? versus HA: ?? ≠ ?? at the ? = 5% significance level.

(a) Based upon the confidence interval, what is your conclusion of the hypothesis test? Explain.

(b) Can we use the above confidence interval without any additional information to conduct the hypothesis test at the ? = 10% level? Why or why not?

Answer 1

A 95% confidence interval for ?? − ?? is (-4.5, -0.15).

Based upon the data from which the confidence interval was constructed,

someone wants to test

H0: ?? = ?? versus HA: ?? ≠ ??

i.e

H0:- ?? - ?? = 0 vs Ha:-  ?? - ?? ≠ 0

at the ? = 5% significance level.

(a) Based upon the confidence interval, what is your conclusion of the hypothesis test?

We reject Ho when the Confidence interval does not contain the null hypothesis value. ( 0 in this case)

Here  95% confidence interval for ?? − ?? is (-4.5, -0.15).

which does not contain 0.

So we reject Ho.

We may conclude that the mean of the two variables are different

b)

Can we use the above confidence interval without any additional information to conduct the hypothesis test at the ? = 10% level?

No, we cannot use the above 95% confidence interval for testing of hypothesis for level = 0.10

because in 95 % confidence interval we have used level 0.05.which can be conclude at 5% level.

for level 0.10 conclusion we have to calculate the 90% confidence interval.