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

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.

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:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

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

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

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?

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

$M = 1.96\frac{198}{\sqrt{81}}$

$M = 43.12$

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.