Click here to open the distribution applet An investigator wishes to determine w
ID: 3064802 • Letter: C
Question
Click here to open the distribution applet An investigator wishes to determine whether alcohol consumption causes deterioration in the performance of automobile drivers. Before the driving test, subjects drank a glass of orange juice which, in the case of the treatment group, is laced with three ounces of vodka. Performance is measured by the number of errors made on a driving simulator. There were seventy eight volunteer subjects which were randomly assigned, in equal numbers, to the two groups. For subjects in the treatment group, the mean number of errors (X1) equals 21 and the standard deviation (S1) equals 15.51. For subjects in the control group, the mean number of errors (x2) equals 11, and the standard deviation (S2) equals 11.23. Test the claim that alcohol consumption causes deterioration in the performance of automobile drivers. a= P-value=Explanation / Answer
Given that,
mean(x)=21
standard deviation , s.d1=15.51
number(n1)=78
y(mean)=11
standard deviation, s.d2 =11.23
number(n2)=78
null, Ho: u1 = u2
alternate, H1: u1 > u2
level of significance, = 0.1
from standard normal table,right tailed t /2 =1.293
since our test is right-tailed
reject Ho, if to > 1.293
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =21-11/sqrt((240.5601/78)+(126.1129/78))
to =4.6122
| to | =4.6122
critical value
the value of |t | with min (n1-1, n2-1) i.e 77 d.f is 1.293
we got |to| = 4.6122 & | t | = 1.293
make decision
hence value of | to | > | t | and here we reject Ho
p-value:right tail - Ha : ( p > 4.6122 ) = 0.00001
hence value of p0.1 > 0.00001,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 > u2
test statistic: 4.6122
critical value: 1.293
decision: reject Ho
p-value: 0.00001
alcohal consumption causes deterioration in the perfomence of automobile drivers
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