A data set includes 107 body temperatures of healthy adult humans for which x ov

Question

A data set includes 107 body temperatures of healthy adult humans for which x overbar = 98.7 degrees F and s = 0.72 degrees Upper F. Complete parts (a) and (b) below.

What is the best point estimate of the mean body temperature of all healthy humans?

The best point estimate is­­­­_______ degrees F

Using the sample statistics, construct a 99% confidence interval estimate of the mean body temperature of all healthy humans. Do the confidence interval limits contain 98.6 degrees F? What does the sample suggest about the use of 98.6 degrees F as the mean body temperature?

_____ degrees F < mu <_______ degrees F

Do the confidence interval limits contain 98.6degrees F? YES or NO

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

This suggests that the mean body temperature could be higher than98.6 degrees F.

This suggests that the mean body temperature could very possibly be98.6 degrees F.

This suggests that the mean body temperature could be lower than 98.6degrees F.

Explanation / Answer

A data set includes 107 body temperatures of healthy adult humans for which x overbar = 98.7 degrees F and s = 0.72 degrees Upper F. Complete parts (a) and (b) below.

What is the best point estimate of the mean body temperature of all healthy humans?

IT IS THE SAMPLE MEAN, 98.7 degrees F. [ANSWER]

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Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.005          
X = sample mean =    98.7          
z(alpha/2) = critical z for the confidence interval =    2.575829304          
s = sample standard deviation =    0.72          
n = sample size =    107          
              
Thus,              
              
Lower bound =    98.52070933          
Upper bound =    98.87929067          
              
Thus, the confidence interval is              
              
(   98.52070933   ,   98.87929067   ) [ANSWER]

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Do the confidence interval limits contain 98.6degrees F? YES [ANSWER]

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

This suggests that the mean body temperature could very possibly be98.6 degrees F. [ANSWER]

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