Question: Assume the temperature increase in the coolant follows a Normal distribution. A physical model suggests that the average temperature increase in the water used as coolant in a compressor chamber should not be more than 5 degree C. Temperature increases in the coolant measured on 9 independent runs of the compressing unit revealed the following data:

6.4 4.3 5.6 4.9 5.5 5.9 6.4 5.1 6.2

a) Construct a 95% confidence interval for the mean increase of the temperature in the coolant.

b) Construct a 90% confidence interval for the variance of temperature increase in the coolant.