A random sample of 100 automobile owners in the state of Virginia shows that an automobile is driven on average 23,500 kilometers per year with a standard deviation of 3900 kilometers. Construct a 99\% confidence interval for the average number of kilometers an automobile is driven annually in Virginia. What can we assert with 99\% confidence about the possible size of our error if we estimate the average number of kilometers driven by car owners in Virginia to be 23,500 kilometers per year?

UkusakazaL 2021-08-04 Answered
A random sample of 100 automobile owners in the state of Virginia shows that an automobile is driven on average 23,500 kilometers per year with a standard deviation of 3900 kilometers.
Assume the distribution of measurements to be approximately normal.
a) Construct a 99% confidence interval for the average number of kilometers an automobile is driven annually in Virginia.
b) What can we assert with 99% confidence about the possible size of our error if we estimate the average number of kilometers driven by car owners in Virginia to be 23,500 kilometers per year?
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Answers (1)

question2answer
Answered 2021-08-17 Author has 155 answers

a) The 99% confidence interval for the average number of kilometres an automobile is driven is obtained below:
The value of mean is 23,500 kilometres, population standard deviation is 3,900 and sample size (n)=100
Critical value:
From the standard normal distribution table, for the 99% confidence level the critical values is (z)2.58.
The confidence interval formula for the population mean is,
C.I.=x±zσn
Substitute mean =23,500, standard deviation (σ) is 3,900 and sample size (n)=100.
C.I.=x±zσn
=23,500±2.583.900100
=23,500±2.58(390)
=23,500±1006.2
=(23,5001006.2, 23,500+1006.2)
=(22,493.8, 24,506.2)
Thus, the 99% confidence interval for the average number of kilometres an automobile is between 22,493.8 and 24,506.2.
b) The required formula is obtained below:
ME=zα2(σn)
Substitute 3,900 for σ, 100 for n and 2.58 for Zα2.
ME=2.58(3,900100)
=2.58(3,90010)
=2.58(390)
=1006.2
With 99% confidence that the possible size of our error will not exceed the 1006.2 kilometres.

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