You are a researcher interested in how nursing care affects the number of days t
ID: 2926909 • Letter: Y
Question
You are a researcher interested in how nursing care affects the number of days that heart transplant patients stay in the hospital. You believe that the better the nursing care the fewer days they spend in-patient. We track the days spent in-patient of two independent samples who recieved heart transplants. Group one (X1) had their transplants at the teaching hospital associated with Wottsamatta U. While the other group (X2) had their transplants at Apathetic General. Based on your negative opinion of the care people get at Apathetic General, you have an "a-priori" assumption about which group will get better faster and so stay fewer days:
Here is the data:
X1 X2
24 18
23 23
16 29
17 30
19 31
13 29
17 26
20 21
15 24
26 19
Compute a pooled t test (Which uses an estimated or pooled standard error of the difference between the means) Show all the testing steps and answer the research question.
Explanation / Answer
H0 : Mean stay at teaching hospital is equal to mean stay at apathetic hospital. X1 = X2
Ha : Mean stay at teaching hospital is less than the mean stay at apathetic hospital.X1 < X2
Sample mean for X1 = x1 = 19 days
sample mean for X2 = x2 = 25 days
standard deviation for X1 = s1 = 4.21637 days
standard deviation for X2 = s2 = 4.4721 days
Pooled standard deviation sp = sqrt [(s12 + s2 2)/2 ] = sqrt [(42 + 4.47212)/2 ] = 4.4721 days
Pooled standard error of the difference between the means = sp sqrt (1/n1 + 1/n2 ) = 4.4721 * sqrt (1/10 + 1/10)
= 2
Test statistic
t = (25 - 19)/ 2 = 3
for dF = 10 + 10 -2 = 18 and dF =0.5
tcr = 1.734
p - value = 0.0038 < 0.05
so t > tcr so we shall reject the null hypothesis and can conclude that the research is correct and hospital who have emphatic attitude and have better nursing care have less mean time of stay for heart transplant.
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