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Vikki [24]
3 years ago
7

consider the following scenario: Assume daily protein intake values in a population of athletes are known to have a standard dev

iation 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.
Mathematics
1 answer:
Kipish [7]3 years ago
5 0

Answer:

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 \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{58.6}{\sqrt{267}} = 7.03

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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