A team of scientists are investigating whether a new drug will decrease the amou

Question

A team of scientists are investigating whether a new drug will decrease the amount of errors in attention during a driving exam. A random sample was taken from a population of people, with a u = 16, at a driving school and were given the new drug. The amount of errors after treatment for the n = 10 sample is as follows: 10, 12, 15, 11, 10, 9, 8, 10, 10, 11. Does the drug help decrease driving errors. Perform a one-tailed test at alpha = .01.

A.  H0: u <=(less than or equal to) 16. H1: u > 16 B.  H0: u >=(greater than or equal to) 16. H1: u < 16 C.  H0: u = 16. H1: u =/(does not equal) 16

Explanation / Answer

Given that,
population mean(u)=16
sample mean, x =10.6
standard deviation, s =1.8974
number (n)=10
null, Ho: >=16
alternate, H1: <16
level of significance, = 0.01
from standard normal table,left tailed t /2 =2.821
since our test is left-tailed
reject Ho, if to < -2.821
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =10.6-16/(1.8974/sqrt(10))
to =-9
| to | =9
critical value
the value of |t | with n-1 = 9 d.f is 2.821
we got |to| =9 & | t | =2.821
make decision
hence value of | to | > | t | and here we reject Ho
p-value :left tail - Ha : ( p < -8.9998 ) = 0
hence value of p0.01 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: >=16
alternate, H1: <16 , H0: u >=(greater than or equal to) 16. H1: u < 16
test statistic: -9
critical value: -2.821
decision: reject Ho
p-value: 0

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