The management of Regional Hospital has made substantial improvements in their h
ID: 3130172 • Letter: T
Question
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 from before and after the improvements. At 95% confidence, test to determine if there has been a significant reduction in the average length of stay.
a. State the Null and Alternative hypotheses
b. Find the Interval estimator
c. Compute the test stat
e. What is your conclusion and what do you conclude?
After Before Sample Size 45 58 Sample Mean (in days) 4.6 4.9 Standard Deviation 0.5 06Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u1 - u2 >= 0
Ha: u1 - u2 < 0 [ANSWER]
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b)
At level of significance = 0.05
As we can see, this is a left tailed test.
As
n1 = sample size of group 1 = 45
n2 = sample size of group 2 = 58
Thus, df = n1 + n2 - 2 = 101
Now, the critical value for t is
tcrit = - 1.66008063 [ANSWER, CRITICAL VALUE]
[Hi! If "interval estimator" refers to something else in your class, please resubmit this question together with the definition of interval estimator in your class. That way we can continue helping you! Thanks!]
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c)
Calculating the means of each group,
X1 = 4.6
X2 = 4.9
Calculating the standard deviations of each group,
s1 = 0.5
s2 = 0.6
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 45
n2 = sample size of group 2 = 58
Also, sD = 0.108454839
Thus, the t statistic will be
t = [X1 - X2 - uD]/sD = -2.766128305 [ANSWER]
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d)
where uD = hypothesized difference = 0
Also, using p values,
p = 0.003373168 [ANSWER]
As P < 0.05, we reject Ho.
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e)
Hence, there is significant evidence at 0.05 level that the average length of stay in RFH is significantly less than the average length of stay in GH. [CONCLUSION]
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Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!
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