Question

Based on interviews with 94 SARS​ patients, researchers found that the mean incubation period was 4.6 ​days, with a standard deviation of 15.4 days. Based on this​ information, construct a​ 95% confidence interval for the mean incubation period of the SARS virus. Interpret the interval.

Answer 1

Solution:

Confidence interval for population mean() using t distribution  

Given that,

= 4.6 ....... Sample mean

s = 15.4 ........Sample standard deviation

n = 94 ....... Sample size

Note that, Population standard deviation() is unknown..So we use t distribution.

Our aim is to construct 95% confidence interval.

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.05 2 = 0.025

Also, n = 94

d.f= n-1 = 93

     =    = = 1.986  

( use t table or t calculator to find this value..)

Now , confidence interval for mean() is given by:

  

15.4 - 1.986*(15.4/ 94)      15.4 + 1.986*(15.4/ 94)

15.4 - 3.1545 < < 15.4 + 3.1545

12.2455 < < 18.5545

is the required 95% confidence interval for mean.