A research neurologist is testing the effect of a drug on response time by injec

Question

A research neurologist is testing the effect of a drug on response time by injecting 25 rats with a unit dose of the drug, subjecting each to a neurological stimulus, and recording its response time. The neurologist knows that the mean time for rats not injected with the drug (the "control" mean) is 2.5 seconds. She wishes to test whether the mean response time for drug-injected rats differs from 2.5 seconds.

The sampling experiment is conducted with the following results:

Sample size, n=25; Mean response time= 2.75 seconds; standard deviation= 0.5 seconds.

Conduct a Test of hypothesis, using a= 0.1. [We assume the population is normally distributed.]

Explanation / Answer

Given that,
population mean(u)=2.5
sample mean, x =2.75
standard deviation, s =0.5
number (n)=25
null, Ho: =2.5
alternate, H1: !=2.5
level of significance, = 0.1
from standard normal table, two tailed t /2 =1.711
since our test is two-tailed
reject Ho, if to < -1.711 OR if to > 1.711
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =2.75-2.5/(0.5/sqrt(25))
to =2.5
| to | =2.5
critical value
the value of |t | with n-1 = 24 d.f is 1.711
we got |to| =2.5 & | t | =1.711
make decision
hence value of | to | > | t | and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 2.5 ) = 0.0197
hence value of p0.1 > 0.0197,here we reject Ho
ANSWERS
---------------
null, Ho: =2.5
alternate, H1: !=2.5
test statistic: 2.5
critical value: -1.711 , 1.711
decision: reject Ho
p-value: 0.0197

we have enough evidence to support the claim that the mean response time for drug-injected rats differs from 2.5 seconds

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