Question

Based on interviews with 87 SARS​ patients, researchers found that the mean incubation period was 4.6 days, with a standard deviation of 14.7

days. Based on this​ information, construct a​ 95% confidence interval for the mean incubation period of the SARS virus. Interpret the interval.

1. The lower bound is ??? days (round to two decimals as needed)

2. The upper bound is ??? days (round to two decimals as needed)

3. Interpret the interval and choose the correct answer

a). There is 95% confidence the mean incubation period is less than the lower bound of the interval

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

c). There is 95% confidence that the mean incubation period is greater than the upper bound of the interval.

d). There is 95% probability that the mean incubation period lies between the lower and upper bounds of the interval.

Answer 1

sample mean, xbar = 4.6
sample standard deviation, s = 14.7
sample size, n = 87
degrees of freedom, df = n - 1 = 86

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 1.988

ME = tc * s/sqrt(n)
ME = 1.988 * 14.7/sqrt(87)
ME = 3.133

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (4.6 - 1.988 * 14.7/sqrt(87) , 4.6 + 1.988 * 14.7/sqrt(87))
CI = (1.47 , 7.73)

1). The lower bound is 1.47 days

2. The upper bound is 7.73 day

3)

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