Problem 7 The owner of a gasoline station wants to study gasoline purchasing hab
ID: 3179083 • Letter: P
Question
Problem 7 The owner of a gasoline station wants to study gasoline purchasing habits of motorists
at his station. He selects a random sample of of 60 motorists during a certain week, with the
following results: The amount purchased was x = 11.3 gallons, s=3.1 gallons. Ten motorists
purchased premium-grade gasoline. = 0.05.
a. Is there evidence that the population mean purchase was greater than 10 gallons?
b. Is there evidence that the population mean purchase was less than 10 gallons?
c. Is there evidence that the population mean purchase was different than 10 gallons?
d. Is there evidence that the percentage of all the motorists at the station who purchased premium-
grade gasoline is less than 20%? What is the p-value?
Explanation / Answer
a.
Given that,
population mean(u)=10
sample mean, x =11.3
standard deviation, s =3.1
number (n)=60
null, Ho: <10
alternate, H1: >10
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.671
since our test is right-tailed
reject Ho, if to > 1.671
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =11.3-10/(3.1/sqrt(60))
to =3.248
| to | =3.248
critical value
the value of |t | with n-1 = 59 d.f is 1.671
we got |to| =3.248 & | t | =1.671
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 3.2483 ) = 0.00096
hence value of p0.05 > 0.00096,here we reject Ho
ANSWERS
---------------
null, Ho: =10
alternate, H1: >10
test statistic: 3.248
critical value: 1.671
decision: reject Ho
p-value: 0.00096
[ANSWER]
there is evidence that the population mean purchase was greater
than 10 gallons
c.
critical value
the value of |t | with n-1 = 59 d.f is 2.001
we got |to| =3.248 & | t | =2.001
make decision
hence value of | to | > | t | and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 3.2483 ) = 0.0019
hence value of p0.05 > 0.0019,here we reject Ho
ANSWERS
---------------
null, Ho: =10
alternate, H1: !=10
test statistic: 3.248
critical value: -2.001 , 2.001
decision: reject Ho
p-value: 0.0019
evidence that the population mean purchase was different than 10 gallons