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 ≈ 14°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 (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 fall.It will go up because hot air will make the balloon rise. It will go down because hot air will make the balloon rise.It will go up because hot air will make the balloon fall.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

100%

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 ≈ 14°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

(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 fall.It will go up because hot air will make the balloon rise. It will go down because hot air will make the balloon rise.It will go up because hot air will make the balloon fall.

Expert Solution

Step 1

$\mathbf{Solution}$

$\mathrm{\mathbf{given}:}$

$\mathrm{Sample\;size\;(n)=56}$

$\mathrm{Sample\;mean\;(\bar x)=97}$

$\mathrm{Population\;standard\; deviation\;(\sigma)=14}$

Since population standard deviation is known, Use z-distribution to find z-critical value.

${\color{Blue} \mathbf{(a)}}\;\mathbf{For \;95\% \;confidence \;level, \;z_{\frac{\alpha }{2}}=1.960}$

$\mathbf{Download\;link\;for\;excel\;to\;find\;z_{\frac{\alpha }{2}}:}$

https://drive.google.com/file/d/1S_b_En4yZMZPhsaGfBA2eE_M0IJFOVeW/view?usp=sharing

$\mathrm{\mathbf{formula:}\;Confidence\;interval\;for\;the\;population\;mean,\;\mu}$

$\mathrm{=\bar x \pm \left [ \frac{z_{\frac{\alpha }{2}}*\sigma}{\sqrt{n}} \right ]}$

Plug in all the values in the formula, we get

$\mathrm{=97 \pm \left [ \frac{1.960*14}{\sqrt{56}} \right ]}$

$\mathrm{=97 \pm 3.7}$

$\mathrm{lower\;limit=97-3.7=\mathbf{{\color{Red} 93.3}}\;^{o}C}$

$\mathrm{upper\;limit=97+3.7=\mathbf{{\color{Red} 100.7}}\;^{o}C}$

Step by step

Solved in 2 steps with 15 images

Knowledge Booster

$Inequality$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions