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 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: 57.3 35.7 54.5 56.8 51.1 70.8 77.3 51.6 54.7 63.6 59.2 59.2 55.8 38.2

CO: 44.7 52.1 60.2 52.7 47.2 65.6 71.4 48.8 53.1 66.3 59.8 47.5 64.5 34.6

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 CL CO. Round your test statistic to two decimal places and your P-value to three decimal places.)

t=

df =

P-value =

Explanation / Answer

Given that,
mean(x)=56.1286
standard deviation , s.d1=10.8463
number(n1)=14
y(mean)=54.8929
standard deviation, s.d2 =10.1688
number(n2)=14
null, Ho: u1 < u2
alternate, H1: u1 > u2
level of significance, = 0.01
from standard normal table,right tailed t /2 =2.65
since our test is right-tailed
reject Ho, if to > 2.65
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =56.1286-54.8929/sqrt((117.64222/14)+(103.40449/14))
to =0.311
| to | =0.311
critical value
the value of |t | with min (n1-1, n2-1) i.e 13 d.f is 2.65
we got |to| = 0.31098 & | t | = 2.65
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value:right tail - Ha : ( p > 0.311 ) = 0.38037
hence value of p0.01 < 0.38037,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 > u2
test statistic: 0.311
critical value: 2.65
decision: do not reject Ho
p-value: 0.38037

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