Question

Suppose that a psychologist is interested in performance on a cognitive task under sleep-deprived and rested conditions among 10 participants. Performance will be measured by the number of errors made by the participants in each condition. The researcher believes that more errors will be made under the sleep-deprived condition. Her observations are reported below. Use the 7 steps of null hypothesis testing to test her hypothesis, set alpha at .01. For this problem, M_D = -3.1 and SE_D = 3.14

            Rested                         Sleep Deprived

            6                                              11

            9                                              14

            4                                              12

            6                                              10

            9                                              9

            8                                              13

            6                                              7

            8                                              5

            3                                              5

            6                                              10

Answer 1

Given that,
mean(x)=6.5
standard deviation , s.d1=2.0138
number(n1)=10
y(mean)=9.6
standard deviation, s.d2 =3.134
number(n2)=10
null, Ho: u1 = u2
alternate, H1: u1 < u2
level of significance, α = 0.01
from standard normal table,left tailed t α/2 =2.821
since our test is left-tailed
reject Ho, if to < -2.821
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =6.5-9.6/sqrt((4.05539/10)+(9.82196/10))
to =-2.6315
| to | =2.6315
critical value
the value of |t α| with min (n1-1, n2-1) i.e 9 d.f is 2.821
we got |to| = 2.63153 & | t α | = 2.821
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value:left tail - Ha : ( p < -2.6315 ) = 0.01365
hence value of p0.01 < 0.01365,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 < u2
test statistic: -2.6315
critical value: -2.821
decision: do not reject Ho
p-value: 0.01365
we do not have enough evidence to support the claim that The researcher believes that more errors will be made under the sleep-deprived condition.