An investigator wishes to determine whether alcohol consumption causes deteriora

Question

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 four ounces of vodka. Performance is measured by the number of errors made on a driving simulator. There were one hundred and seventy-two 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 17 and the standard deviation (s1) equals 14.37. For subjects in the control group, the mean number of errors (x2) equals 10, and the standard deviation (s2) equals 18.47. Test the claim that alcohol consumption causes deterioration in the performance of automobile drivers.

T=

P-value=

Explanation / Answer

Given that,
mean(x)=17
standard deviation , s.d1=14.37
number(n1)=86
y(mean)=10
standard deviation, s.d2 =18.47
number(n2)=86
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.1
from standard normal table, two tailed t /2 =1.663
since our test is two-tailed
reject Ho, if to < -1.663 OR if to > 1.663
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =17-10/sqrt((206.4969/86)+(341.1409/86))
to =2.774
| to | =2.774
critical value
the value of |t | with min (n1-1, n2-1) i.e 85 d.f is 1.663
we got |to| = 2.77396 & | t | = 1.663
make decision
hence value of | to | > | t | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 2.774 ) = 0.007
hence value of p0.1 > 0.007,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 2.774
critical value: -1.663 , 1.663
decision: reject Ho
p-value: 0.007

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