The dotplot shows the results of taking 300 SRSs of 10 temperature readings from a Normal population with μ = 50 and σ = 3 and recording the sample standard deviation s_x each time. Suppose that the standard deviation from an actual sample is sx=5°F. What would you conclude about the thermostat manufacturer’s claim? Explain your reasoning.

During the winter months, outside temperatures at the Starneses’ cabin in Colorado can stay well below freezing (32°F, or 0°C) for weeks at a time. To prevent the pipes from freezing, Mrs. Starnes sets the thermostat at 50°F. The manufacturer claims that the thermostat allows variation in home temperature that follows a Normal distribution with σ = 3°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 μ = 50°F and standard deviation σ = 3°F.

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1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Sz = simulated sample standard deviation of temperature (°F)