Based on interviews with 84 SARS patients, researchers found that the mean incub

Question

Based on interviews with 84 SARS patients, researchers found that the mean incubation period was 5 days, with a standard deviation of 15.5 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 nothing days. (Round to two decimal places as needed.) The upper bound is nothing days. (Round to two decimal places as needed.) Interpret the interval. Choose the correct answer below. A. There is 95% confidence that the mean incubation period is greater than the upper bound of the interval. B. There is 95% confidence that the mean incubation period lies between the lower and upper bounds of the interval. C. There is a 95% probability that the mean incubation period lies between the lower and upper bounds of the interval. D. There is 95% confidence that the mean incubation period is less than the lower bound of the interval.

Explanation / Answer

a.
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=5
Standard deviation( sd )=15.5
Sample Size(n)=84
Confidence Interval = [ 5 ± Z a/2 ( 15.5/ Sqrt ( 84) ) ]
= [ 5 - 1.96 * (1.691) , 5 + 1.96 * (1.691) ]
= [ 1.685,8.315 ]

LB = 1.69
UP = 8.32

b.
C. There is a 95% probability that the mean incubation period lies between the lower and upper bounds of the interval

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