Which of the following is true A If a 90 CI for the mean is

Which of the following is true?

A.

If a 90% CI for the mean is (75.3 to 80.9), we would reject H0: Mean=70 in favor of H1: Mean?70 at alpha=0.05.

B.

If a test is run and p=0.0356, then we can reject H0 at alpha=0.01.

C.

If a 95% CI for the difference in two independent means is (-4.5 to 2.1), then the point estimate is -2.1.

D.

If a 95% CI for the difference in two independent means is (2.1 to 4.5), there is no significant difference in means.

E.

The margin of error is always greater than or equal to the standard error.

Solution

A.

If a 90% CI for the mean is (75.3 to 80.9), we would reject H0: Mean=70 in favor of H1: Mean?70 at alpha=0.05.

It is assumed Mean >70 for H1.

True

B.

B.

If a test is run and p=0.0356, then we can reject H0 at alpha=0.01.

As p > 0.01, accept null hypothesis.

--Hence false.

C.

C.

If a 95% CI for the difference in two independent means is (-4.5 to 2.1), then the point estimate is -2.1.

Point estimate = -1.2, Hence false

d)

D.

If a 95% CI for the difference in two independent means is (2.1 to 4.5), there is no significant difference in means.

False (since 0 is not in this interval)

e)

E.

The margin of error is always greater than or equal to the standard error.

Margin of error = z alpha/2 * std error

Hence >= std error if z alpha/2 >=1

Generally we take for 90% 95%99% where z alpha/2 >1

Hence true.