# A sample of 25 general practicians (GPs) in Adelaide hospitals were surveyed and it was found...

## Question:

A sample of 25 general practicians (GPs) in Adelaide hospitals were surveyed and it was found that the average time they had spent with a patient was 17.3 minutes. Based on a large number of similar surveys, it was known that the standard deviation of time spent with a patient is 4.1 minutes. The lower and upper limits of a 99% confidence interval for the population meantime (in minutes) spent with a patient in Adelaide hospitals would be

a) (15.4, 19.2)

b) (16.9, 17.7)

c) (15.2, 19.4)

d) (15.0, 15.6)

## Confidence Interval for a Mean:

The confidence interval is a type of interval estimation that gives a range of all possible values likely to be true population mean at a stated level of confidence. The upper and lower bounds of the interval occur plus and minus margin of error from the best point estimate (sample mean).

The correct answer is: c) (15.2, 19.4).

Given that;

{eq}n=25\\\bar x=17.3\\\sigma=4.1 {/eq}

Use equation below to construct 99% confidence interval for the population mean:

{eq}\displaystyle \left(\bar X\pm Z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}\right) {/eq}

Find critical value that corresponds to 99% level of confidence:

{eq}\displaystyle \frac{\alpha}{2}=\frac{1-0.99}{2}=0.005\\z_{0.005}=\pm 2.58 {/eq}

Plug in values into the formula and solve for upper and lower bounds:

{eq}\displaystyle \left(17.3\pm 2.58\times \frac{4.1}{\sqrt{25}}\right)\\(17.3\pm 2.12)\\(15.2, 19.4) {/eq}