# How many rounds of golf do those physicians who play golf play per year? A survey of 12...

## Question:

How many rounds of golf do those physicians who play golf play per year? A survey of 12 physicians revealed the following numbers:

7,41,13,4,30,36,19,14,18,30,14,47

Estimate with 97% confidence the mean number of rounds played per year by physicians, assuming that the population is normally distributed with a standard deviation of 8.

Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits. Confidence Interval =

## Confidence Interval:

In this question we will use the t distribution to construct the 97% confidence interval for the mean number of rounds played per year by physicians. We are using the t distribution because the sample size is very small and the population standard deviation is not known.

Given that,

Sample size, {eq}n = 12 {/eq}

 7 41 13 4 30 36 19 14 18 30 14 47

Sample mean is defined as:

{eq}\bar{x} = \frac{\sum{x_i}}{n} {/eq}

Excel function for the sample mean:

=AVERAGE(7,41,13,4,30,36,19,14,18,30,14,47)

{eq}\bar{x} = 22.75 {/eq}

Sample standard deviation is defined as:

{eq}s = \sqrt{\frac{\sum{(x_i - \bar{x})^2}}{n-1}} {/eq}

Excel function for the sample standard deviation:

=STDEV(7,41,13,4,30,36,19,14,18,30,14,47)

{eq}s = 13.77 {/eq}

The 97% confidence interval for the population mean is defined as:

{eq}\bar{x} \pm t_{0.03/2}\times \frac{s}{\sqrt{n}} {/eq}

Excel function for the confidence coefficient:

=TINV(0.03,11)

{eq}22.75 \pm 2.491\times \frac{13.77}{\sqrt{12}}\\ 12.89 < \mu < 32.612 {/eq}

97% confidence the mean number of rounds played per year by physicians = (12.89, 32.612).