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 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 52 readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, σ ≈ 18°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.)

lower limit °C

upper limit °C

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 97

Population standard deviation = = 18

Sample size = n = 52

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96.

Margin of error = E = Z_/2* ( /n)

= 1.96 * ( 18 / 52)

= 4.9

At 95% confidence interval estimate of the population mean is,

- E < < + E

97 - 4.9 < < 97 + 4.9

92.1 < < 101.9

( 92.1, 101.9 )

Lower Limit = 92.1 ⁰ C

Upper Limit = 101.9⁰ C