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dolphi86 [110]
3 years ago
8

A supplier of a certain car parts chain of stores wants to estimate the average length of time car owners plan to keep their car

s. From the past it is known that the standard deviation of the length of times car owners plan to keep their cars is 6.5 years. A random sample of 25 car owners results the average length of time of 7.2 years. Calculate and interpret a 99% confidence interval for the average length of time all car owners plan to keep their cars.
Mathematics
1 answer:
____ [38]3 years ago
7 0

Answer:

The 99% confidence interval for the average length of time all car owners plan to keep their cars is between 3.85 years and 10.55 years.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.99}{2} = 0.005

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.005 = 0.995, so z = 2.575

Now, find the margin of error M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 2.575*\frac{6.5}{\sqrt{25}} = 3.35

The lower end of the interval is the sample mean subtracted by M. So it is 7.2 - 3.35 = 3.85 years

The upper end of the interval is the sample mean added to M. So it is 7.2 + 3.35 = 10.55 years

The 99% confidence interval for the average length of time all car owners plan to keep their cars is between 3.85 years and 10.55 years.

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