Question

Based on interviews with 82 SARS​ patients, researchers found that the mean incubation period was 5.1 days, with a standard deviation of 15.7 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 :

Given that,

Point estimate = sample mean = = 5.1

sample standard deviation = s = 15.7

sample size = n = 82

Degrees of freedom = df = n - 1 = 82-1=81

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,81 = 1.990

Margin of error = E = t_/2,df * (s /n)

= 1.990 * (15.7 / 82)

= 3.5

The 95% confidence interval estimate of the population mean is,
- E < < + E

5.1 - 3.5 < < 5.1 + 3.5

1.6 < < 8.6

( 1.6,8.6 )

First we find the degrees of freedom by the formula n - 1,then find t-value.then find margin of error by the formula t_/2,df * (s /n) result is ME is 3.5,then we find the 95% confidence interval by the formula
- E < < + E then answer is ( 1.6 , 8.6 )