Body temperatures of humans (in degrees Fahrenheit) have a known standard deviat
ID: 3317677 • Letter: B
Question
Body temperatures of humans (in degrees Fahrenheit) have a known standard deviation of = 0.75 degree. A random sample of 23 people yielded a mean of x = 98.6 degrees with a sample standard deviation of s= 0.70 degrees. It is known that the human body temperatures has a normal distribution. We want to estimate the true average human body temperature, , (in degrees Fahrenheit).
a)What is the critical value for a 97.5% confidence interval for ?
b) Create a 97.5% confidence interval for
c) How many observations would we need to guarantee that the 97.5% confidence interval has has a length of 0.2 or less?
d) Create a 97.5% prediction interval for the body temperature of a single human.
e) Assuming is not known, create a 97.5% confidence interval for using this data.
Explanation / Answer
Solution
(a) Z critical value at 97.5% = +-2.242
(b) 97.% confidence interval = (sample mean +- z0.0125( /n0.5)
= (98.6+-2.242(0.75/230.5)
97.5% CI = (98.25, 98.95)
(c) 2* Margin of error = 0.2
so, 0.1 = 2.242*(0.75/n0.5)
n = 283
(d) 97.5% CI = (98.6+-2.242(0.75))
= (96.92, 100.28)
(e) 97.5% CI = (98.6+-2.242(0.7/230.5)
= (98.27,98.93)