Solution Found!
Solved: Exercises 13 and 14 refer to the following setting. During the winter months
Chapter 7, Problem 13(choose chapter or problem)
During the winter months, outside temperatures at the Starneses cabin in Colorado can stay well below freezing (\(32^{\circ} \mathrm{F}\), or \(0^{\circ} \mathrm{C}\)) for weeks at a time. To prevent the pipes from freezing, Mrs. Starnes sets the thermostat at \(50^{\circ} \mathrm{F}\). The manufacturer claims that the thermostat allows variation in home temperature that follows a Normal distribution with \(\sigma=3^{\circ} \mathrm{F}\). To test this claim, Mrs. Starnes programs her digital thermometer to take an SRS of \(n=10\) readings during a 24-hour period. Suppose the thermostat is working properly and that the actual temperatures in the cabin vary according to a Normal distribution with mean \(\mu=50^{\circ} \mathrm{F}\) and standard deviation \(\sigma=3^{\circ} \mathrm{F}\).
The Fathom screen shot below shows the results of taking 500 SRSs of 10 temperature readings from a population distribution that is N(50, 3) and recording the sample variance \(s_{x}^{2}\) each time.
(a) Describe the approximate sampling distribution.
(b) Suppose that the variance from an actual sample is \(s_{x}^{2}=25\). What would you conclude about the thermostat manufacturers claim? Explain.
Questions & Answers
QUESTION:
During the winter months, outside temperatures at the Starneses cabin in Colorado can stay well below freezing (\(32^{\circ} \mathrm{F}\), or \(0^{\circ} \mathrm{C}\)) for weeks at a time. To prevent the pipes from freezing, Mrs. Starnes sets the thermostat at \(50^{\circ} \mathrm{F}\). The manufacturer claims that the thermostat allows variation in home temperature that follows a Normal distribution with \(\sigma=3^{\circ} \mathrm{F}\). To test this claim, Mrs. Starnes programs her digital thermometer to take an SRS of \(n=10\) readings during a 24-hour period. Suppose the thermostat is working properly and that the actual temperatures in the cabin vary according to a Normal distribution with mean \(\mu=50^{\circ} \mathrm{F}\) and standard deviation \(\sigma=3^{\circ} \mathrm{F}\).
The Fathom screen shot below shows the results of taking 500 SRSs of 10 temperature readings from a population distribution that is N(50, 3) and recording the sample variance \(s_{x}^{2}\) each time.
(a) Describe the approximate sampling distribution.
(b) Suppose that the variance from an actual sample is \(s_{x}^{2}=25\). What would you conclude about the thermostat manufacturers claim? Explain.
ANSWER:
Step 1 of 3
Given that, suppose the thermostat is working properly and that the actual temperatures in the cabin vary according to a Normal distribution with mean \(\mu=50^{\circ} \mathrm{F}\) and standard deviation \(\sigma=3^{0} F\).
The Fathom screen shot below shows the results of taking 500 SRSs of 10 temperature readings from a population distribution that is N(50, 3) and recording the sample variance \(s_{x}^{2}\) each time.
