Question

The dataset ICUAdmissions includes information on 200 patients admitted to an Intensive Care Unit. One of the variables, Status, indicates whether each patient lived (indicated with a 0) or died (indicated with a 1). Use technology and the dataset to construct a 90% confidence interval for the proportion of ICU patients who live. Click here for the datset associated with this question.

Round your answers to three decimal places.

The 90% confidence interval is

Answer 1

TRADITIONAL METHOD
given that,
possible chances (x)=100
sample size(n)=200
success rate ( p )= x/n = 0.5
I.
sample proportion = 0.5
standard error = Sqrt ( (0.5*0.5) /200) )
= 0.035
II.
margin of error = Z a/2 * (standard error)
where,
Za/2 = Z-table value
level of significance, α = 0.1
from standard normal table, two tailed z α/2 =1.645
margin of error = 1.645 * 0.035
= 0.058
III.
CI = [ p ± margin of error ]
confidence interval = [0.5 ± 0.058]
= [ 0.442 , 0.558]
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DIRECT METHOD
given that,
possible chances (x)=100
sample size(n)=200
success rate ( p )= x/n = 0.5
CI = confidence interval
confidence interval = [ 0.5 ± 1.645 * Sqrt ( (0.5*0.5) /200) ) ]
= [0.5 - 1.645 * Sqrt ( (0.5*0.5) /200) , 0.5 + 1.645 * Sqrt ( (0.5*0.5) /200) ]
= [0.442 , 0.558]
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interpretations:
1. We are 90% sure that the interval [ 0.442 , 0.558] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 90% of these intervals will contains the true population proportion
Answer:
90% confidence interval for the proportion of ICU patients who live [ 0.442 , 0.558]