How hot is the air in the top (crown) of a hot air balloon? Information from Bal

Question

How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds, by Worth and Young (Random House), claims that the air in the crown should be an average of 100 degree C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100 degree C. What is the a reasonable and sale range of temperatures? This range may vary with the size and (decorative) shape of the balloon. All balloons have a temperature gauge in the crown. Suppose that 50 readings (for a balloon in equilibrium) gave a mean temperature of x = 97 degree C. For this balloon, sigma = 16 degree C. (a) Compute a 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium. (b) If the average temperature in the crown of the balloon goes above the high end of your confidence interval, do you expect that the balloon will go up or down? Explain. It will go down because hot air will make the balloon rise. It will go up because hot air will make the balloon rise. It will go down because hot air will make the balloon fall. It will go up because hot air will make the balloon fall.

Explanation / Answer

Answers for the question here:

a. The 95% computation is give by:

Lower limit = Sample.Mean - Sigma*Stdev
= 97 - 1.96*16
=65.64

Upper limit = Sample.Mean + Sigma*Stdev
= 97 + 1.96*16
=128.36

b.

If the average temperature in the crown of balloon foes above the high end
of your confidence interval then the balloon wll go up bevause hot air will make
the balloon rise.

Hence, the answer is B. It will do up because hot air will make the balloon rise

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