Question

3) The director of a medical hospital feels that her surgeons perform fewer operations per year than the national average of 211. She selected a random sample of 15 surgeons and found that the mean number of operations they performed was 208.8. The standard deviation of the sample was 3.8. Is there enough evidence to support the director’s feelings at α = 0.10? Assume the variable is normally distributed.

a) State the appropriate null and alternate hypotheses.

b) Compute the value of the test statistic (Provide the answer with 3 decimal places).

c) What is the critical value?

d) Based on part c) do you reject H0?

e) Write your conclusion.

Answer 1

Given
X bar	208.8
μ0	211
S	3.8
n	15

a)Hypothesis :		α=	0.1
		df	14	n-1
Ho:	μ1​ = μ0
Ha:	μ1​ < μ0
c) t Critical Value :
tc	-1.345030374	T.INV(D1,9)	LEFT
ts	<=	tc	LEFT	To reject
b)Test :
t	-2.242253516	(X bar-μ )/(S/SQRT(n))
P value :
p	0.020828846	T.DIST(ts,df,TRUE)	LEFT
Decision :
P value	<	α	Reject H0

d)

t stat < t critical, Reject H0

P value < 0.1, Reject H0

e)

There is enough evidence to conclude that director of a medical hospital surgeons perform fewer operations per year than the national average of 211