Question

Head movement evaluations are important because disabled individuals may be able to operate communications aids using head motion. A paper reported the accompanying data on neck rotation (in degrees) for 14 subjects both in the clockwise direction (CL) and in the counterclockwise direction (CO). For purposes of this exercise, you can assume that the 14 subjects are representative of the population of adult Americans.

Subject:	1	2	3	4	5	6	7	8	9	10	11	12	13	14
CL:	57.4	35.7	54.5	56.8	51.1	70.8	77.3	51.6	54.7	63.6	59.2	59.2	55.8	38.5
CO:	44.6	52.1	60.2	52.7	47.2	65.6	71.4	48.8	53.1	66.3	59.8	47.5	64.5	34.3

Based on these data, is it reasonable to conclude that mean neck rotation is greater in the clockwise direction than in the counterclockwise direction? Carry out a hypothesis test using a significance level of 0.01. (Use a statistical computer package to calculate the P-value. Use μ_d = μ_CL − μ_CO. Round your test statistic to two decimal places and your P-value to three decimal places.)

t	=
df	=
P-value	=

State your conclusion.

We reject H₀. We have no evidence that mean neck rotation is greater in the clockwise direction than in the counterclockwise direction.

We do not reject H₀. We have convincing evidence that mean neck rotation is greater in the clockwise direction than in the counterclockwise direction.     

We do not reject H₀. We have no evidence that mean neck rotation is greater in the clockwise direction than in the counterclockwise direction.

We reject H₀. We have convincing evidence that mean neck rotation is greater in the clockwise direction than in the counterclockwise direction.

Answer 1

since data is paired data

so we have

n=14 sample mean of difference =m=1.29

sample SD of difference =S=7.77

we have to test that mean of clockwise is more than that of anti-clock wise so

so test statistics is given by

df=n-1=14-1=13

since test is two tailed so

P-Value =P(t>0.62)=0.273

since P Value is more than level of significance hence we failed to reject H0 so there is no enough evidence to conclude that clockwise mean is more than that of anticlockwise hence

We do not reject H0. We have no evidence that mean neck rotation is greater in the clockwise direction than in the counterclockwise direction.