Question

The lengths, in inches, of adult corn snakes are normally distributed with a population standard deviation of 8 inches and an unknown population mean. A random sample of 25 snakes is taken and results in a sample mean of 58 inches.

What is the correct interpretation of the confidence interval?

Select the correct answer below:

1. We can estimate with 99% confidence that the true population mean length of adult corn snakes is between 53.88 and 62.12 inches.

2. We can estimate with 99% confidence that the sample mean length of adult corn snakes is between 53.88 and 62.12 inches.

3. We can estimate that 99% of adult corn snakes will have a length that is between 53.88 and 62.12 inches.

Answer 1

Answer:

1. We can estimate with 99% confidence that the true population mean length of adult corn snakes is between 53.88 and 62.12 inches.

Step-by-step explanation:

With the data that, we have, we can estimate the 99% confidene interval for the true population mean.

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 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.

$M = 2.575*\frac{8}{\sqrt{25}} = 4.12$

The lower end of the interval is the sample mean subtracted by M. So it is 58 - 4.12 = 53.88 inches.

The upper end of the interval is the sample mean added to M. So it is 58 + 4.12 = 62.12 inches

So the correct answer is:

1. We can estimate with 99% confidence that the true population mean length of adult corn snakes is between 53.88 and 62.12 inches.