Question

Based on interviews with 95 SARS patients, researchers found that the mean incubation period was 4.1 days with a standard deviation of 14.1 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

(1)

SE = s/

= 14.1/

= 1.4466

ndf = n - 1 = 95 - 1 = 94

= 0.05

From Table, critical values of t = 1.9855

The lower bound = 4.1 - (1.9855 X 1.4466) = 4.1 - 2.8723 = 1.23

So,

The lower bound is 1.23

(2)

The upper bound = 4.1 + (1.9855 X 1.4466) = 4.1 + 2.8723 = 6.97

So,

The upper bound is 6.97

(3) Correct option:

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