A data set includes 103 body temperatures of healthy adult humans for which x ov
ID: 3176497 • Letter: A
Question
A data set includes 103 body temperatures of healthy adult humans for which x overbar = 98.1 degrees F and s = 0.56 degrees F.
Complete parts (a) and (b) below.
a. What is the best point estimate of the mean body temperature of all healthy humans?
The best point estimate is ____ degrees F. (Type an integer or a decimal.)
b. 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 98.6degrees F? What does the sample suggest about the use of 98.6degrees F as the mean body temperature?
What is the confidence interval estimate of the population mean mu?
_____degrees F < mu < ____ degrees F (Round to three decimal places as needed.)
Do the confidence interval limits contain 98.6degrees F?
Yes
No
What does this suggest about the use of 98.6degrees F as the mean body temperature?
A. This suggests that the mean body temperature could very possibly be 98.6degrees F.
B. This suggests that the mean body temperature could be higher than 98.6degrees F.
C. This suggests that the mean body temperature could be lower than 98.6 degrees F.
Explanation / Answer
a.The dataset contains 103 observations. Hence we can assume that the sample follows normal distribution .And hence the best point estimate of the mean body temparature of all healthy humans will be same as the sample mean which is 98.1 degrees F.
b. Assuming the body temparature of all healthy humans follow a normal distribution. From central limit theorem mean = x overbar = 98.1 degrees F.
Since the standard deviation for all healthy humans is not known. We take the standard deviation of the sample divided by the square root of sample size as the best estimate of population standard deviation as per central limit theorem
s of population = 0.56 degrees F / square root of 103 = 0.055
From the normal distribution table 99% confidence interval the values falling inside the range is 98.1 +/- 2.576 standard deviation
lower limit = 98.1 - 2.576*0.055 = 97.958 and upper limit = 98.1 + 2.576 * 0.055 = 98.242
99% confidence interval = 97.958 degrees F < 98.1 < 98.242
the confidence interval does not contain 98.6 degrees F.
C. This suggests that the mean body temperature could be lower than 98.6 degrees F.