# Based on interviews with 99 SARS patients, researchers found that the mean incubation period was...

## Question:

Based on interviews with {eq}99 {/eq} SARS patients, researchers found that the mean incubation period was {eq}5.5 {/eq} days, with a standard deviation of {eq}14.3 {/eq} days. Based on this information, construct a {eq}95 \% {/eq} confidence interval for the mean incubation period of the SARS virus. Interpret the interval.

## Confidence Interval for a Proportion:

Confidence interval gives range of value likely to be true population proportion at given level of confidence. If population standard deviation is unknown, we use student t distribution.

Given that;

{eq}n=99\\\bar x=5.5\\s=14.3 {/eq}

Use equation below to construct 95% confidence interval:

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

Find critical value t that correspond to n-1 degrees of freedom and 1-CL level of significance:

{eq}t_{0.05,df=98}=\pm 1.984 {/eq}

Plug in values into the formula and calculate upper and lower bounds of 95% confidence interval:

{eq}\displaystyle \left(5.5\pm 1.98\times \frac{14.3}{\sqrt{99}}\right)\\(5.5\pm 2.85)\\(2.65, 8.35) {/eq}