Head movement eva nications aids using head motion. A reported the accompanying

Question

Head movement eva nications aids using head motion. A 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 adult Americans. of the population of Subject: 23 4 5 6 789 10 11 12 13 14 CL: 57.5 35.7 54.5 56.8 51.1 70.8 77.3 51.6 54.7 63.6 59.2 9.2 55.8 38.8 co: 44.5 52.1 60.2 52.7 47.2 65.6 71.4 48.8 53.1 66.3 59.8 47.5 64.5 34.1 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 Pevalue. Use p - co. Round your test statistic to two decimal places and your P-value to three decimal places.) df m P-value State your conclusion. We reject Ho. We have convincing evidence that mean neck rotation is greater in the clockwise direction than in the counterclockwise direction. O We reject Ho. We have no evidence that mean neck rotation is greater in the clockwise direction than in the counterclockwise direction. o we do not reject Ho, we have convincing evidence that mean neck rotation is greater in the clockwise direction than in the counterclockwise direction We do not reject Ho. We have no evidence that mean neck rotation is greater in the clockwise direction than in the direction.

Explanation / Answer

Using R software we have,

CODE:

cl <- c(57.5,35.7,54.5,56.8,51.1,70.8,77.3,51.6,54.7,63.6,59.2,59.2,55.8,38.8)
co <- c(44.5,52.1,60.2,52.7,47.2,65.6,71.4,48.8,53.1,66.3,59.8,47.5,64.5,34.1)
t.test(cl,co,alternative = "greater", conf.level = 0.99,paired = T)

OUTPUT:

> cl <- c(57.5,35.7,54.5,56.8,51.1,70.8,77.3,51.6,54.7,63.6,59.2,59.2,55.8,38.8)
> co <- c(44.5,52.1,60.2,52.7,47.2,65.6,71.4,48.8,53.1,66.3,59.8,47.5,64.5,34.1)
> t.test(cl,co,alternative = "greater", conf.level = 0.99,paired = T)

Results of Hypothesis Test
--------------------------

Null Hypothesis: difference in means = 0

Alternative Hypothesis: True difference in means is greater than 0

Test Name: Paired t-test

Estimated Parameter(s): mean of the differences = 1.342857

Data: cl and co

Test Statistic: t = 0.6438124

Test Statistic Parameter: df = 13

P-value: 0.2654459

99% Confidence Interval: LCL = -4.185129
UCL = Inf

So, t = 0.6438124,

df =13,

p-value = 0.2654459.

b) Here p-value is greater than 0.01. So, we do not reject H0. We have no evidence that mean neck rotation is greater in clockwise direction than in the counterclockwise direction.

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