Question

The heights of dogs, in inches, in a city are normally distributed with a population standard deviation of 4 inches and an unknown population mean. If a random sample of 18 dogs is taken and results in a sample mean of 32 inches, find the error bound (EBM) of the confidence interval with a 90% confidence level.

Answer 1

Answer:

The error bound (EBM) of the confidence interval with a 90% confidence level is 1.55 inches.

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:

$\alpha = \frac{1-0.9}{2} = 0.05$

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 $1-0.05 = 0.95$, so $z = 1.645$

Now, find the margin of error, or error bound, M as such

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

So

$M = 1.645*\frac{4}{\sqrt{18}} = 1.55$

The error bound (EBM) of the confidence interval with a 90% confidence level is 1.55 inches.