Assume that you know the average speed of cars on a highway is 55mph and it\'s p

Question

Assume that you know the average speed of cars on a highway is 55mph and it's population standard error of the mean is 4mph. In order to prove whether the average car speed on that highway has changed or not you took a sample of 25 cars, and found their average speed is 60.4mph and the sample standard deviation to be 10mph
At a 10% significance level, your conclusion for the null hypothesis of the average car speed unchanged is.
A. Reject the null hypothesis B. Accept the null hypothesis C. Inconclusive D. Fail to reject the null hypothesis E. Only b and d Assume that you know the average speed of cars on a highway is 55mph and it's population standard error of the mean is 4mph. In order to prove whether the average car speed on that highway has changed or not you took a sample of 25 cars, and found their average speed is 60.4mph and the sample standard deviation to be 10mph
At a 10% significance level, your conclusion for the null hypothesis of the average car speed unchanged is.
A. Reject the null hypothesis B. Accept the null hypothesis C. Inconclusive D. Fail to reject the null hypothesis E. Only b and d
At a 10% significance level, your conclusion for the null hypothesis of the average car speed unchanged is.
A. Reject the null hypothesis B. Accept the null hypothesis C. Inconclusive D. Fail to reject the null hypothesis E. Only b and d

Explanation / Answer

Given that,
population mean(u)=55
Standard Error= sd/ Sqrt(n)
Where,
sd = Standard Deviation
n = Sample Size
Standard deviation( sd )=7.4
Sample Size(n)=25
Standard Error = 4
4 = sd/ Sqrt(25)
sd = 5 * 4 = 20
standard deviation, =20
sample mean, x =60.4
number (n)=25
null, Ho: =55
alternate, H1: >55
level of significance, = 0.1
from standard normal table,right tailed z /2 =1.282
since our test is right-tailed
reject Ho, if zo > 1.282
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 60.4-55/(20/sqrt(25)
zo = 1.35
| zo | = 1.35
critical value
the value of |z | at los 10% is 1.282
we got |zo| =1.35 & | z | = 1.282
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : right tail - ha : ( p > 1.35 ) = 0.08851
hence value of p0.1 > 0.08851, here we reject Ho
ANSWERS
---------------
null, Ho: =55
alternate, H1: >55
test statistic: 1.35
critical value: 1.282
decision: reject Ho
p-value: 0.08851

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---