Question

In: Statistics and Probability

Which of the following is TRUE? A. The confidence interval is narrower if the level of...

Which of the following is TRUE?

A.

The confidence interval is narrower if the level of significance is smaller.
B.

The confidence interval is wider if the level of confidence level is larger.
C.

The confidence interval is narrower if the sample size is smaller.
D.

The confidence interval is wider if the sample size is larger.

Solutions

Expert Solution

Solution:- (B)

The True statements is:

(B) The confidence interval is wider if the level of confidence level is larger.

Confidence interval depends upon the margin of error.

Formula for the margin of error is:

Margin of error is directly proportional to confidence level.

The false statements are:

(A) The confidence interval is narrower if the level of significance is smaller.

Confidence interval depends upon the margin of error.

Formula for the margin of error is:

Margin of error is inversely proportional to significance level.

(C) The confidence interval is narrower if the sample size is smaller.

Margin of error is inversely proportional to sample size. Hence the confidence interval is narrower if the sample size is larger.

(D) The confidence interval is wider if the sample size is larger.

Margin of error is inversely proportional to sample size. Hence the confidence interval is wider if the sample size is smaller.

orchestra answered 1 year ago
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