Question

Answer true or false to each statement concerning a confidence interval for a population mean. Give reasons for your answers. a. The length of a confidence interval can be determined if you know only the margin of error. b. The margin of error can be determined if you know only the length of the confidence interval. c. The confidence interval can be obtained if you know only the margin of error. d. The confidence interval can be obtained if you know only the margin of error and the sample mean.

Answer 1

Answer:

(a) True

(b) True

(c) False

(d) True

Step-by-step explanation:

The general form of a confidence interval is:

$CI=SS\pm MOE$

Here,

SS = Sample statistic

MOE = margin of error

The formula to compute the MOE is:

$MOE=\frac{length}{2}$

Here, length implies the length of the confidence interval.

(a)

The statement is:

"The length of a confidence interval can be determined if you know only the margin of error."

The length of the confidence interval is twice the MOE.

So, yes one can compute the length of the confidence interval if they know the value if MOE.

The statement is True.

(b)

The statement is:

"The margin of error can be determined if you know only the length of the confidence interval."

The margin of error of the confidence interval is half the length.

So, yes one can compute the MOE if they know the length of the confidence interval.

The statement is True.

(c)

The statement is:

"The confidence interval can be obtained if you know only the margin of error."

The confidence interval formula is:

$CI=SS\pm MOE$

So, if we only knew the value of MOE we cannot compute the confidence interval. We will also need the value of the sample statistic.

The statement is False.

(d)

The statement is:

"The confidence interval can be obtained if you know only the margin of error and the sample mean"

The confidence interval formula is:

$CI=SS\pm MOE$

So, if we knew the value of MOE and the sample statistic we can compute the confidence interval.

The statement is True.