The average gasoline price of one of the major oil companies has been $2.20 per
ID: 3228644 • Letter: T
Question
The average gasoline price of one of the major oil companies has been $2.20 per gallon. Because of cost reduction measures, it is believed that there has been a significant reduction in the average price. In order to test this belief, we randomly selected a sample of 36 of the company's gas stations and determined that the average price for the stations in the sample was $2.14. Assume that the standard deviation of the population (s) is $0.12. a. State the null and the alternative hypotheses. b. Compute the test statistic. c. What is the p-value associated with the above sample results? d. At 95% confidence, test the company's claim.Explanation / Answer
Given that,
population mean(u)=2.2
standard deviation, =0.12
sample mean, x =2.14
number (n)=36
null, Ho: =2.2
alternate, H1: <2.2
level of significance, = 0.05
from standard normal table,left tailed z /2 =1.645
since our test is left-tailed
reject Ho, if zo < -1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 2.14-2.2/(0.12/sqrt(36)
zo = -3
| zo | = 3
critical value
the value of |z | at los 5% is 1.645
we got |zo| =3 & | z | = 1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : left tail - ha : ( p < -3 ) = 0.00135
hence value of p0.05 > 0.00135, here we reject Ho
ANSWERS
---------------
null, Ho: =2.2
alternate, H1: <2.2
test statistic: -3
critical value: -1.645
decision: reject Ho
p-value: 0.00135
it is proven that it is been a significant reduction in the average price
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