Based on interviews with 96 SARS patients researchers found

Based on interviews with 96 SARS patients, researchers found that the mean incubation period was 5 days, with a standard deviation of 14.9 days. Construct a 95% confidence interval for the mean incubation period of the SARS virus. Interpret the interval. The lower bound is ____days? The upper bound is __days?

Solution

We use t-distribution because the population standard deviation is not known.

95% CI for µ using t-distribution

We assume that sample is taken from an approximately normal population and that sample are random.

Sample mean = x=5

Sample standard deviation = =14.9

Sample size= n=96

Significance level==1-0.95=0.05

Degrees of freedom for t-distribution df=n-1=96-1=95

Critical value= = 1.98525

Margin of error=E= * =3.03486

Limits of 95% confidence interval are given by

Lower limit = x-E=5- 3.03486=1.9651

upper limit = x-E=5+ 3.03486=8.0349

hence the 95% CI is (1.9651,8.0349)