Right Hand Left Hand 138138 126126 106106 152152 157157 182182 185185 199199 183

Question

Right Hand

Left Hand

138138

126126

106106

152152

157157

182182

185185

199199

183183

206206

What is the test statistic? t= ? (round to 3 places)

Several students were tested for reaction times (in thousandths of a second) using their right and left hands. (Each value is the elapsed time between the release of a strip of paper and the instant that it is caught by the subject.) Results from five of the students are included in the graph to the right. Use a .10
significance level to test the claim that there is no difference between the reaction times of the right and left hands.

Explanation / Answer

Given that,
mean(x)=153.8
standard deviation , s.d1=33.056
number(n1)=5
y(mean)=173
standard deviation, s.d2 =33.5261
number(n2)=5
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.1
from standard normal table, two tailed t /2 =2.132
since our test is two-tailed
reject Ho, if to < -2.132 OR if to > 2.132
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =153.8-173/sqrt((1092.69914/5)+(1123.99938/5))
to =-0.912
| to | =0.912
critical value
the value of |t | with min (n1-1, n2-1) i.e 4 d.f is 2.132
we got |to| = 0.91187 & | t | = 2.132
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -0.9119 ) = 0.413
hence value of p0.1 < 0.413,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: -0.912
critical value: -2.132 , 2.132
decision: do not reject Ho
p-value: 0.413
the claim that there is no difference between the reaction times of the right and left hands.

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