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?