The temperature of a certain solution is estimated by taking a large number of independent measurements and averaging them. The estimate is 37°C, and the uncertainty (standard deviation) in this estimate is 0.1°C.
a. Find a 95% confidence interval for the temperature.
b. What is the confidence level of the interval 37 ± 0.1°C?
c. If only a small number of independent measurements had been made, what additional assumption would be necessary in order to compute a confidence interval?
d. Making the additional assumption, compute a 95% confidence interval for the temperature if 10 measurements were made.
(a) 
=37 , and the uncertainty is 
. A 95% confidence interval is 37 ± 1.96(0.1), or (36.804, 37.196).
(b) Since 
this confidence interval is of the form 
The area to the left of z = 1 is approximately 0.1587. Therefore ?/2 = 0.1587, so the level is 1?? = 0.6826, or approximately 68%.
(c) The measurements come from a normal population.
(d) 
= 2.262. A 95% confidence interval is therefore 
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