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The average annual cost of the first year of owning and caring for a cat is $1,500. A sample of 81 will be used. Based on past studies, the population standard deviation is assumed known with σ = $198. What is the margin of error for a 95% confidence interval of the mean cost of the first year of owning and caring for a cat?

User Mina Jacob
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1 Answer

19 votes
19 votes

Answer:

The margin of error for a 95% confidence interval of the mean cost of the first year of owning and caring for a cat is of $43.12.

Explanation:

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


image

Now, we have to find z in the Ztable as such z has a pvalue of
image.

That is z with a pvalue of
image, so Z = 1.96.

Now, find the margin of error M as such


image

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

Sample of 81

This means that
image

What is the margin of error for a 95% confidence interval of the mean cost of the first year of owning and caring for a cat?


image


image


image

The margin of error for a 95% confidence interval of the mean cost of the first year of owning and caring for a cat is of $43.12.

User Agentnega
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