Question

Based on interviews with 93 SARS​ patients, researchers found that the mean incubation period was 4.4 ​days, with a standard deviation of 15.2 days. Based on this​ information, construct a​ 95% confidence interval for the mean incubation period of the SARS virus. Interpret the interval.

Use technology to create a​ 95% confidence interval based on the statistics from this sample using the​ t-distribution. Note that the sample size must be large ​(greater than or equals≥​30)or the population must be normally distributed.

Identify the values of ^---x , ​s, and n given in the problem.

- x	?
s	?
n	?

Determine the lower​ bound, rounding to two decimal places.

Determine the upper​ bound, rounding to two decimal places.

(1−α)•100% confidence interval constructed from (1−α)•100% of all simple random samples of size n from the population whose parameter is unknown will contain the parameter.

Interpret the confidence interval.

Answer 1

= 4.4

s = 15.2

n = 93

At 95% confidence interval the critical value is t^* = 1.986

The 95% confidence interval is

+/- t^* * s/

= 4.4 +/- 1.986 * 15.2/

= 4.4 +/- 3.13

= 1.27, 7.53

Lower bound = 1.27

Upper bound = 7.53

We are 95% confident that the true population mean of incubation period of the SARS virus lies between the interval 1.27 and 7.53.