Question

The weights, in pounds, of dogs in a city are normally distributed with a population standard deviation of 2 pounds and an unknown population mean. A random sample of 16 dogs is taken and results in a sample mean of 28 pounds. Identify the parameters needed to calculate a confidence interval at the 90% confidence level. Then find the confidence interval.

Answer 1

Answer:

Parameters:

$z = 1.645, \sigma = 2, n = 16$

The 90% confidence interval for the weights, in pounds, of dogs in a city is between 27.1775 pounds and 27.8225 pounds.

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 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.

$M = 1.645*\frac{2}{\sqrt{16}} = 0.8225$

The lower end of the interval is the sample mean subtracted by M. So it is 28 - 0.8225 = 27.1775 pounds

The upper end of the interval is the sample mean added to M. So it is 28 + 0.8225 = 27.8225 pounds

The 90% confidence interval for the weights, in pounds, of dogs in a city is between 27.1775 pounds and 27.8225 pounds.