Question

Based on interviews with 93 SARS​ patients, researchers found that the mean incubation period was 4.1 ​days, with a standard deviation of 15.3 days. Based on this​ information, construct a​ 95% confidence interval for the mean incubation period of the SARS virus. Interpret the interval.

The lower bound is..

the upper bound is..

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 4.1

sample standard deviation = s = 15.3

sample size = n = 93

Degrees of freedom = df = n - 1 = 93 - 1 = 92

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,92 = 1.986

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

= 1.986 * (15.3 / 93)

= 3.151

The 95% confidence interval estimate of the population mean is,

- E < < + E

4.1 - 3.151 < < 4.1 + 3.151

0.949 < < 7.251

The lower bound is 0.949

The upper bound is 7.251