Head movement evaluations are important because disabled individuals may be able

Question

Head movement evaluations are important because disabled individuals may be able to operate communication 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. 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 mu_cl - mu_Co. Round your test statistic to two decimal places and your P-value to three decimal places.) t = df = P-value =

Explanation / Answer

For clockwise data,

Mean = 56.157

Standard Deviation = 10.836

For counter clockwise data,

Mean = 54.871

Standard deviation = 10.207

So, t = (Mean_CL - Mean_CO)/sqrt(S_CL^2/n + S_CO^2/n) = (56.157 - 54.871)/sqrt(10.836^2 / 14 + 10.207^2/ 14) = 0.32

df = (S_CL^2/n + S_CO^2/n)^2/((S_CL^2/n)^2 / (n-1) + (S_CO^2/n)^2 /(n-1) )

= (10.836^2 /14 + 10.207^2/14)^2 / (((10.836^2 / 14)^2) /13 + ((10.207^2/14)^2)/13)

=25.9 = 26

p value = 0.376

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