Question

The ICU-Admissions dataset includes a variable indicating the age of the patient. Find and interpret a 90% confidence interval for mean age of ICU patients using the facts that, in the sample, the mean is 55.75 years and the standard error for such means is SE = 1.64. The sample size of 100 is large enough to use a normal distribution

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 55.75

SE =1.64
Sample size = n =100

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E = Z/2    * ( /n)

=Z/2    * SE

= 1.645 * 1.64

= 2.7
At 90% confidence interval
is,

- E < < + E

55.75 - 2.7 <   < 55.75+ 2.7

53.05 <   < 58.45

( 53.05, 58.45)