The management of Regional Hospital has made substantial improvements in their hospital and would like to test and determine whether there has been a significant decrease in the average length of stay of their patients in their hospital. The following data has been accumulated before and after the improvements. At the 5% level, test to determine if there has been a significant reduction in the average length of stay. After Before Sample size 45 58 Mean (in days) 4.6 4.9 Standard Deviation (σ) .5 .6 a. Formulate the hypotheses. b. Compute the test statistic. c. Using the p-value approach, test to see if there has been a significant reduction in the average length of stay. Let α = .05.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
- The management of Regional Hospital has made substantial improvements in their hospital and would like to test and determine whether there has been a significant decrease in the average length of stay of their patients in their hospital. The following data has been accumulated before and after the improvements. At the 5% level, test to determine if there has been a significant reduction in the average length of stay.
|
|
After |
Before |
|
|
45 |
58 |
|
Mean (in days) |
4.6 |
4.9 |
|
Standard Deviation (σ) |
.5 |
.6 |
|
a. |
Formulate the hypotheses. |
|
b. |
Compute the test statistic. |
|
c. |
Using the p-value approach, test to see if there has been a significant reduction in the average length of stay. Let α = .05. |
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