Question

Based on interviews with 88 SARS​ patients, researchers found that the mean incubation period was 4.4 ​days, with a standard deviation of 14.8 days. Based on this​ information, construct a​ 95% confidence interval for the mean incubation period of the SARS virus. Interpret the interval.

Lower Bound:

Upper Bound:

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 4.4

Population standard deviation =    =14.8

Sample size n =88

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
=1.96 * ( 14.8 / 88 )

= 3.09
At 95% confidence interval mean
is,

- E < < + E

4.4 -3.09 <   < 4.4+ 3.09

1.31 <   < 7.49

(1.31 , 7.49)