1. A researcher is testing the effect of a new cold and flu medication on mental
ID: 2932550 • Letter: 1
Question
1. A researcher is testing the effect of a new cold and flu medication on mental alertness. A sample of n = 9 college students is obtained and each student is given the normal dose of the medicine. Thirty minutes later, each student's performance is measured on a video game that requires careful attention and quick decision-making. The scores for the nine students are as follows: 6, 8, 10, 6, 7, 13, 5, 5, 3. Assuming that scores for students in the regular population average = 10, are the data sufficient to conclude that the medication has a significant effect on mental performance? Conduct a simple t-test at the .05 level of significance. Construct a 95% confidence interval.Explanation / Answer
Given that,
population mean(u)=10
sample mean, x =7
standard deviation, s =3
number (n)=9
null, Ho: =10
alternate, H1: !=10
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.306
since our test is two-tailed
reject Ho, if to < -2.306 OR if to > 2.306
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =7-10/(3/sqrt(9))
to =-3
| to | =3
critical value
the value of |t | with n-1 = 8 d.f is 2.306
we got |to| =3 & | t | =2.306
make decision
hence value of | to | > | t | and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -3 ) = 0.0171
hence value of p0.05 > 0.0171,here we reject Ho
ANSWERS
---------------
null, Ho: =10
alternate, H1: !=10
test statistic: -3
critical value: -2.306 , 2.306
decision: reject Ho
p-value: 0.0171
we have singinificant effect on medical performence
b.
given that,
sample mean, x =7
standard deviation, s =3
sample size, n =9
level of significance, = 0.05
from standard normal table, two tailed value of |t /2| with n-1 = 8 d.f is 2.306
we use CI = x ± t a/2 * (sd/ Sqrt(n))
where,
x = mean
sd = standard deviation
a = 1 - (confidence level/100)
ta/2 = t-table value
CI = confidence interval
confidence interval = [ 7 ± Z a/2 ( 3/ Sqrt ( 9) ]
= [ 7-(2.306 * 1) , 7+(2.306 * 1) ]
= [ 4.694 , 9.306 ]
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