Inferential Statistics One Sample T-Test – used to compare mean to a standard. A
ID: 2921794 • Letter: I
Question
Inferential Statistics
One Sample T-Test – used to compare mean to a standard.
A researcher wants to determine if the ALOS for patients treated for CHF with major complications and comorbidities is shorter or longer than the US average of 3.6 days. The consultant selects 37 patients having this DRG and calculates the hospitals’ ALOS is 4.9 days with a standard deviation (s) of 3.0 days. Test the hypothesis that this hospital’s ALOS is significantly different from the US average at an alpha level () of 0.05.
What is ALOS for this hospital and what are the degrees of freedom of the data?
State the null and alternate hypothesis for the one sample t-test:
For a two-sided test, calculate alpha/2 then look up the t-distribution critical value in the textbook table for the nearest degrees of freedom you calculated.
Alpha/2=
critical value =
Calculate the t-statistic. T =
Would you accept or reject the null hypothesis? And what can you conclude about whether the hospitals’ ALOS (i.e. 4.9 days) differs significantly from the US average of 3.6?
Explanation / Answer
ALOS = 4.9, df = N - 1 = 37 - 1 = 36
H0: = 3.6, H1: 3.6
Alpha/2 = 0.025
Critical Value = +/- 2.0281
T = (x - )/s/sqrt(N) = (4.9 - 3.6)/(3/sqrt(37)) = 2.6359
Reject the Null hypothesis since T > Critical Value. There is sufficient evidence to suggest hospitals ALOS differs significantly from the US average