Question

Based on interviews with 82 SARS​ patients, researchers found that the mean incubation period was 4.7 ​days, with a standard deviation of 14.6 days. Based on this​ information, construct a​ 95% confidence interval for the mean incubation period of the SARS virus. Interpret the interval.

lower bound ___ days

upper bound ___ days

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 4.7

Population standard deviation =    = 14.6

Sample size n =82

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96 * ( 14.6 / 82)

E= 3.1601
At 95% confidence interval estimate of the population mean
is,

- E < < + E

4.7 -3.1601 <   < 4.7 + 3.1601

1.5399 <   < 7.8601

( 1.5399,7.8601 )

lower bound _1.5399__ days

upper bound _7.8601__ days