In: Statistics and Probability
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..
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 = t0.025,92 = 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