There is some concern that people admitted to the ICU with an infection die at a higher proportion than those admitted without an infection. A random sample of ICU patients was taken. The variables of interest are whether the patient entered the ICU with an infection or not, and whether the patient lived or died. A summary of the data is in the two-way table below. Lived Died Totals Infection 55 21 76 No infection 98 17 115 Totals 153 38 191 Test the claim that the proportion of ICU patients with an infection who died is higher than the proportion of ICU patients without an infection who died at the 0.05 significance level. The null and alternative hypothesis would be: H0:pI=pNH0:pI=pN H1:pI>pNH1:pI>pN H0:pI=pNH0:pI=pN H1:pI≠pNH1:pI≠pN H0:μI=μNH0:μI=μN H1:μI<μNH1:μI<μN H0:μI=μNH0:μI=μN H1:μI≠μNH1:μI≠μN H0:μI=μNH0:μI=μN H1:μI>μNH1:μI>μN H0:pI=pNH0:pI=pN H1:pI
There is some concern that people admitted to the ICU with an infection die at a higher proportion than those admitted without an infection. A random sample of ICU patients was taken. The variables of interest are whether the patient entered the ICU with an infection or not, and whether the patient lived or died. A summary of the data is in the two-way table below. Lived Died Totals Infection 55 21 76 No infection 98 17 115 Totals 153 38 191 Test the claim that the proportion of ICU patients with an infection who died is higher than the proportion of ICU patients without an infection who died at the 0.05 significance level. The null and alternative hypothesis would be: H0:pI=pNH0:pI=pN H1:pI>pNH1:pI>pN H0:pI=pNH0:pI=pN H1:pI≠pNH1:pI≠pN H0:μI=μNH0:μI=μN H1:μI<μNH1:μI<μN H0:μI=μNH0:μI=μN H1:μI≠μNH1:μI≠μN H0:μI=μNH0:μI=μN H1:μI>μNH1:μI>μN H0:pI=pNH0:pI=pN H1:pI
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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There is some concern that people admitted to the ICU with an infection die at a higher proportion than those admitted without an infection.
A random sample of ICU patients was taken. The variables of interest are whether the patient entered the ICU with an infection or not, and whether the patient lived or died. A summary of the data is in the two-way table below.
| Lived | Died | Totals | |
|---|---|---|---|
| Infection | 55 | 21 | 76 |
| No infection | 98 | 17 | 115 |
| Totals | 153 | 38 | 191 |
Test the claim that the proportion of ICU patients with an infection who died is higher than the proportion of ICU patients without an infection who died at the 0.05 significance level.
The null and alternative hypothesis would be:
H0:pI=pNH0:pI=pN
H1:pI>pNH1:pI>pN
H1:pI>pNH1:pI>pN
H0:pI=pNH0:pI=pN
H1:pI≠pNH1:pI≠pN
H1:pI≠pNH1:pI≠pN
H0:μI=μNH0:μI=μN
H1:μI<μNH1:μI<μN
H1:μI<μNH1:μI<μN
H0:μI=μNH0:μI=μN
H1:μI≠μNH1:μI≠μN
H1:μI≠μNH1:μI≠μN
H0:μI=μNH0:μI=μN
H1:μI>μNH1:μI>μN
H1:μI>μNH1:μI>μN
H0:pI=pNH0:pI=pN
H1:pI<pNH1:pI<pN
H1:pI<pNH1:pI<pN
The test is:
right-tailed
left-tailed
two-tailed
The sample statistic is: (to 3 decimals)
The standard error is: (to 3 decimals)
The test statistic is: (to 3 decimals)
The p-value is: (to 3 decimal places)
Based on this we:
- Fail to reject the null hypothesis
- Reject the null hypothesis
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