Question

It is believed that in family physician practices the median amount of time that doctors and physician assistants spend with the patient per appointment is 20 minutes. However, it is claimed that the median amount of time spent with Medicaid patients is less than 20 minutes. A random sample of 12 appointments by Medicaid patients was selected, and the time that the doctor and physician assistants spent with them is recorded below. Test the claim at the 0.025 significance level.

15.6 20.2 18.1 19.5 23.5 20.4 16.2 12.4 9.6 23.8 18.4 14.7

1. Identify the correct HYPOTHESES used in a hypothesis test of the claim.

a.	H0: median = 20 H1: median ≠ 20	b.	H0: median = 20 H1: median > 20
c.		d.	H0: median = 20 H1: median < 20

2. Identify the value of the TEST STATISTIC used in a hypothesis test of the claim.

a.	-0.866	b.	4
c.	1.443	d.	8

3. Identify the value of the CRITICAL VALUE used in a hypothesis test of the claim.

a.	2	b.	0
c.	-1.96	d.	1

4. Identify the CONCLUSION of a hypothesis test of the claim.

a.	There is sufficient evidence to warrant rejection of the claim.	b.	There is not sufficient evidence to warrant rejection of the claim.
c.	There is sufficient evidence to support the claim.	d.	There is not sufficient evidence to support the claim.

Answer 1

1)

H₀: median = 20

H₁: median < 20

2)

X	median	difference=sample1-sample 2
15.6	20	-4.4
20.2	20	0.2
18.1	20	-1.9
19.5	20	-0.5
23.5	20	3.5
20.4	20	0.4
16.2	20	-3.8
12.4	20	-7.6
9.6	20	-10.4
23.8	20	3.8
18.4	20	-1.6
14.7	20	-5.3

number of positive signs=4

number of negative signs=8

test stat = min(+ve, -ve signs) = min(4,8) = 4

3)

The critical value for the signficance level provided and the type of tail is X* = 2.

4)

Since in this case X = 4 >X* = 2, do not reject HO

There is not sufficient evidence to support the claim.