Question

Which of the following statements are not true in developing a confidence interval for the population mean?

a) The width of the confidence interval becomes wider as the confidence level increases.
b) The width of the confidence interval becomes narrower when the sample mean increases.
c) The width of the confidence interval becomes narrower when the sample size n increases.
d) All of the above statements are true.
e) None of the above statements are true.

Answer 1

b) The width of the confidence interval becomes narrower when the sample mean increases.

Explanation:

The confidence interval can be calculated as:

`\bar{x} \pm \text{Test Statistic}\displaystyle(\sigma)/(√(n))`

a) The width of the confidence interval becomes wider as the confidence level increases.

The above statement is true as the confidence level increases the width increases as the absolute value of test statistic increases.

b) The width of the confidence interval becomes narrower when the sample mean increases.

The above statement is false. As the sample mean increases the width of the confidence interval increases.

c) The width of the confidence interval becomes narrower when the sample size n increases.

The above statement is true as the sample size increases the standard error decreases and the confidence interval become narrower.