In a study analyzed by the Statistics Consulting Center at Virginia Tech, a grou

Question

In a study analyzed by the Statistics Consulting Center at Virginia Tech, a group of subjects was asked to complete a certain task on the computer. The response measured was the time to completion. The purpose of the experiment was to test a set of facilitation tools developed by the Department of Computer Science at the university. There were 8 subjects in- volved. With a random assignment, they were given a standard procedure using C language for completion of the task. The sample mean was 164 seconds, and the sample standard deviation was 4.5 seconds. Part a. Support or refute the conjecture at 3% significance level that the mean speed with which the task can be accomplished is greater than 160 seconds. Part b. Now answer using the p-value.

Explanation / Answer

PART A.
Given that,
population mean(u)=160
sample mean, x =164
standard deviation, s =4.5
number (n)=8
null, Ho: =160
alternate,task can be accomplished is greater than 160 seconds H1: >160
level of significance, = 0.03
from standard normal table,right tailed t /2 =2.241
since our test is right-tailed
reject Ho, if to > 2.241
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =164-160/(4.5/sqrt(8))
to =2.514
| to | =2.514
critical value
the value of |t | with n-1 = 7 d.f is 2.241
we got |to| =2.514 & | t | =2.241
make decision
hence value of | to | > | t | and here we reject Ho

ANSWERS
---------------
null, Ho: =160
alternate, H1: >160
test statistic: 2.514
critical value: 2.241
decision: reject Ho

PART B.
p-value :right tail - Ha : ( p > 2.5142 ) = 0.02008
hence value of p0.03 > 0.02008,here we reject Ho
p-value: 0.02008
we have evidence that the mean speed with which the task can be accomplished
is greater than 160 seconds

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