Question

A 95% confidence interval for a population mean is determined to be 100 to 120. If the confidence coefficient is reduced to 0.90, the interval:_________ a. becomes narrower b. becomes wider c. does not change d. becomes 0.1

Answer 1

Answer:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$   (1)

The confidence interval for this case would be:

$100 \leq \mu \leq 120$

And we want to know what happens with the interval if we reduce the confidence level to 90% and for this case we will get a narrower interval since the critical value $t_{\alpha/2}$ would be lower. So then the best option would be:

a. becomes narrower

Step-by-step explanation:

Notation

$\bar X$ represent the sample mean for the sample  

$\mu$ population mean

s represent the sample standard deviation

n represent the sample size  

Solution

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$   (1)

The confidence interval for this case would be:

$100 \leq \mu \leq 120$

And we want to know what happens with the interval if we reduce the confidence level to 90% and for this case we will get a narrower interval since the critical value $t_{\alpha/2}$ would be lower. So then the best option would be:

a. becomes narrower