Question

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?

Answer 1

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
`\alpha` level, that is the subtraction of 1 by the confidence interval divided by 2. So:

`\alpha = (1 - 0.95)/(2) = 0.025`

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

That is z with a pvalue of
`1 - 0.025 = 0.975`, so Z = 1.96.

Now, find the margin of error M as such

`M = z(\sigma)/(√(n))`

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

Sample of 81

This means that
`n = 81`

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?

`M = z(\sigma)/(√(n))`

`M = 1.96(198)/(√(81))`

`M = 43.12`

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.