Question

"You measure 34 dogs' weights, and find they have a mean weight of 67 ounces. Assume the population standard deviation is 13.5 ounces. Based on this, construct a 95% confidence interval for the true population mean dog weight."

Answer 1

Answer:

The 95% confidence interval for the true population mean dog weight is between 62.46 ounces and 71.54 ounces.

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 $1-\alpha$.

So it is z with a pvalue of $1-0.025 = 0.975$, so $z = 1.96$

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.

$M = 1.96*\frac{13.5}{\sqrt{34}} = 4.54$

The lower end of the interval is the sample mean subtracted by M. So it is 67 - 4.54 = 62.46 ounches.

The upper end of the interval is the sample mean added to M. So it is 67 + 4.54 = 71.54 ounces.

The 95% confidence interval for the true population mean dog weight is between 62.46 ounces and 71.54 ounces.