Adata set includes 105 body temperatures of healthy adult humans having a mean of 98.7 degrees f and a standard deviation of 0.64 degrees f.

construct a 99% confidence interval estimate of the mean body temperature of all healthy humans.

what does the sample suggest about the use of 98.6 degrees f as the mean body temperature?

The 99% confidence interval would be given by (98.536;98.864)

We are 99% confident that the true mean body temperature is between (98.536;98.864)    

The value 98.6 is included on the interval but the mid point for the interval is the sample mean 98.7, so for this case 98.6 would be a value to high in order to estimate the population mean, since the best estimator for the population mean is the sample mean on this case .

Step-by-step explanation:

1) 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".

represent the sample mean for the sample  

population mean (variable of interest)

s=0.64 represent the sample standard deviation

n=105 represent the sample size  

Construct a 99% confidence interval estimate of the mean body temperature of all healthy humans.

The confidence interval for the mean is given by the following formula:

  (1)

In order to calculate the critical value we need to find first the degrees of freedom, given by:

Since the Confidence is 0.99 or 99%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,104)".And we see that

Now we have everything in order to replace into formula (1):

So on this case the 99% confidence interval would be given by (98.536;98.864)    

What does the sample suggest about the use of 98.6 degrees F as the mean body temperature?

We are 99% confident that the true mean body temperature is between (98.536;98.864)    

The value 98.6 is included on the interval but the mid point for the interval is the sample mean 98.7, so for this case 98.6 would be a value to high in order to estimate the population mean, since the best estimator for the population mean is the sample mean on this case .

step-by-step explanation:

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