Suppose we want to test whether true population parameter

theta equals a certain number. Consider the following hypothesis test:Upper H 0 : theta equals c Upper H 1 : theta not equals c Where Upper H 0is the null hypothesis, Upper H 1

is the alternative hypothesis, and c a constant. Let theta overbarbe an estimator of

theta.What role does the central limit theorem play in the construction of confidence intervals?

A.

To construct a confidence interval for theta, it is necessary to know the sampling distribution of theta overbar under the null hypothesis.

If the sampling distribution is unknown, the central limit theorem says that it can be approximated by a normal distribution when the sample size n is sufficiently small.

B.

The central limit theorem plays no role in

the construction of confidence intervals

.

C.

The central limit theorem allows us to directly compute the true value of

theta

.

D.

To construct a confidence interval for theta, it is necessary to know the sampling distribution of theta overbar under the null hypothesis.

If the sampling distribution is unknown, the central limit theorem says that it can be approximated by a normal distribution when the sample size n is sufficiently large.