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 Wirth and Young (Random House), claims that the air in the crown should be an average of 100°C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100°C. What is a reasonable and safe 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 56 readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, σ ≈ 22°C.
(a) Compute a 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium. (Round your answers to one decimal place.)
Sample size = n = 56
Z/2 = 1.96
Margin of error = E = Z/2* ( /n)
= 1.96 * (22 / 56)
At 95% confidence interval estimate of the population mean is,
- E < < + E
97 - 5.8< < 97 + 5.8
91.2 < < 102.8
lower limit 91.20C
upper limit 102.80C
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