Hypothesis Testing Imagine that you are studying automobile buyers who choose to
ID: 3326173 • Letter: H
Question
Hypothesis Testing
Imagine that you are studying automobile buyers who choose to replace their current car near the end of its expected lifetime. Specifically, you are interested in how many different dealers late purchasers visit.
Let µ be the mean number of dealers visited by all late replacement buyers. A random sample of 100 late replacement buyers yields a mean and standard deviation of the number of dealers visited of x¯ = 4.32 and s = 0.67.
The test statistic and the corresponding p-values are listed below:
Tasks:
Set up null and alternative hypotheses needed if we wish to attempt to provide evidence that µ differs from 4 dealers.
Identify the test you will apply to test the hypothesis. Justify your choice.
Choose an appropriate level of significance.
Define type I and II errors in the context of your hypotheses.
State your decision regarding the hypothesis.
State the conclusion
Test Statistic p value 4.78 < 0.0001Explanation / Answer
Given that,
population mean(u)=4
standard deviation, =0.67
sample mean, x =4.32
number (n)=100
null, Ho: =4
alternate, H1: !=4
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.95996
since our test is two-tailed
reject Ho, if zo < -1.95996 OR if zo > 1.95996
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 4.32-4/(0.67/sqrt(100)
zo = 4.78
| zo | = 4.78
critical value
the value of |z | at los 5% is 1.95996
we got |zo| =4.78 & | z | = 1.95996
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != 4.78 ) = 0
hence value of p0.05 > 0, here we reject Ho
ANSWERS
---------------
null, Ho: =4
alternate, H1: !=4
test statistic: 4.78
critical value: -1.95996 , 1.95996
decision: reject Ho
p-value: 0
we have enough evidence to support the claim
Type I errors happen when we reject a true null hypothesis
Type II errors happen when we fail to reject a false null hypothesis
so that in this context we reject the null hypothesis,that is type 1 error
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