The post-aesthesia care area (recovery room) at Centre Hospital was recently enlarged. The hope was that with the enlargement the mean number of patients per day would be more than 25. A random sample of 15 days revealed the following number of patients X: X 23 24 25 26 27 28 f 1 3 3 3 2 1 +h マv 290 29
The post-aesthesia care area (recovery room) at Centre Hospital was recently enlarged. The hope was that with the enlargement the mean number of patients per day would be more than 25. A random sample of 15 days revealed the following number of patients X: X 23 24 25 26 27 28 f 1 3 3 3 2 1 +h マv 290 29
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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Please refer to attached image, tq
Transcribed Image Text:The post-aesthesia care area (recovery room) at Centre Hospital was
recently enlarged. The hope was that with the enlargement the mean
number of patients per day would be more than 25. A random sample of
15 days revealed the following number of patients X:
X
23
24
25
26
27
28
29
f
1
2
3
3
3
1
with EX = 390.
(А)
At the 0.05 significance level, examine that the mean number of
patients per day is at most 24. State the necessary assumption(s).
(B)
Assume that the population mean shifts from 24 to 26.5.
Estimate the sample size which is needed for the power of the
test to be 0.9.
Expert Solution
Step 1
A)
Assumptions:
- The population standard deviation is not known.
- The sample size is less than 30.
- The selected samples are independent.
Null Hypothesis:
H0: The mean number of patients per day is at most 24.
Alternative Hypothesis:
H1: The mean number of patients per day is greater than 24.
From the given information,
| X | 23 | 24 | 25 | 26 | 27 | 28 | 29 | |
| f | 1 | 2 | 3 | 3 | 3 | 2 | 1 |
∑f=15 |
| X*f | 23 | 48 | 75 | 78 | 81 | 56 | 29 |
∑X*f=390 |
| X^2*f | 529 | 1152 | 1875 | 2028 | 2187 | 1568 | 841 |
∑X2*f=10180 |
Test statistic:
p value:
Degrees of freedom=n-1=15-1=14
Decision Rule:
If p-value ≤ α, then reject the null hypothesis.
Conclusion:
The level of significance is α=0.05
Here, the p-value is less than the level of significance.
From the decision rule, reject the null hypothesis.
Thus, the mean number of patients per day is greater than 24.
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