Consider the following scenario: Assume daily protein intake values in a population of athletes are known to have a standard deviation of 58.6 grams. From a random sample of size 267 athletes, the mean daily protein intake of 77.0 grams. Find a 95% confidence interval for the population mean daily protein intake. Round final answers to 2 decimal places.

The 95% confidence interval for the population mean daily protein intake is between 69.97g and 84.03g.

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 77 - 7.03 = 69.97g.

The upper end of the interval is the sample mean added to M. So it is 77 + 7.03 = 84.03g.

The 95% confidence interval for the population mean daily protein intake is between 69.97g and 84.03g.

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step-by-step explanation: