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breonnabyers
07.04.2020 •
Mathematics
The percentage of body fat of a random sample of 36 men aged 20 to 29 found a sample mean of 14.42. Find a 95% confidence interval for the mean percentage body fat of all men aged 20 to 29. Assume that percentages of body fat follow a normal distribution with a standard deviation of 6.95.
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Ответ:
So on this case the 95% confidence interval would be given by (12.150;16.690)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
n=36 represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
Since the Confidence is 0.95 or 95%, the value of
and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that ![z_{\alpha/2}=1.96](/tpl/images/0588/0726/6c626.png)
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (12.150;16.690)
Ответ: