Question

17-2: Consider the following­­ set of observations:

10.21   13.65   12.30   9.51     11.32   12.77   6.16     8.55     11.78   12.32

You should not assume these data come from a normal distribution. Test the hypothesis that these data come from a distribution with a median less than or equal to 10.

Answer 1

null hypothesis:		μ̃	=	10
Alternate Hypothesis:		μ̃	<	10

score(xi)	difference=xi-10	Sign
10.21	0.21	+
13.65	3.65	+
12.3	2.3	+
9.51	-0.49	-
11.32	1.32	+
12.77	2.77	+
6.16	-3.84	-
8.55	-1.45	-
11.78	1.78	+
12.32	2.32	+

positive signs ("+") =		7
Negative signs ("-") =		3
test stat T =		3

p value =P(X<=3 |p=0.5) =P(X=0)+P(X=1)+P(X=2)+P(X=3)

=(10C0)*(0.5)¹⁰ +(10C1)*(0.5)¹⁰ +(10C2)*(0.5)¹⁰ +(10C3)*(0.5)¹⁰

= 0.1719

since p value >0.05 , we can not reject null hypothesis

we do not have sufficient evidence at 0.05 level to conclude that these data come from a distribution with a median less than or equal to 10.