Question

g Which statement is true below for the size of the confidence interval for µ? Group of answer choices a. The confidence interval increases as the standard deviation increases. b. The confidence interval increases as the standard deviation decreases. c. The confidence interval increases as the sample size increases. d. The t-value for a confidence interval of 95% is smaller than for a confidence interval of 90%

Answer 1

Answer:

Option a) The confidence interval increases as the standard deviation increases.

Step-by-step explanation:

We have to find the true statements.

Confidence Interval:

$\mu \pm Test_{critical}\frac{\sigma}{\sqrt{n}}$

a. The confidence interval increases as the standard deviation increases.

As the standard deviation increases, the margin of error increases, thus, the width of the confidence interval increases.

Thus, the given statement is true.

b. The confidence interval increases as the standard deviation decreases.

The given statement is false. The explanation is similar to above part.

c. The confidence interval increases as the sample size increases.

As the sample size increases, the margin of error decreases, thus, the confidence interval width decreases.

Thus, the given statement is false.

d. The t-value for a confidence interval of 95% is smaller than for a confidence interval of 90%

The t-value depend on the level of significance as well as degree of freedom. But for a particular degree of freedom  t-value for a confidence interval of 95% is greater than for a confidence interval of 90%.

Thus, the given statement is false.