A confidence interval is constructed for a small sample of temperatures (in degrees Celsius) randomly selected from a normally distributed population for which σ is unknown (such as the data set given in Exercise 10).
a. How is the margin of error E affected if each temperature is converted to the Fahrenheit scale? [F = 9/5C + 32]
b. If the confidence interval limits are denoted by a and b, find expressions for the confidence interval limits after the original temperatures have been converted to the Fahrenheit scale.
c. Based on the results from part (b), can confidence interval limits for the Celsius temperatures be found by simply converting the confidence interval limits from the Celsius scale to the Fahrenheit scale?