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.

Parameters:

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 level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find M as such

In which is the standard deviation of the population and n is the size of the sample.

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.

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step-by-step explanation: