Question

During the winter months, the temperatures at the Colorado cabin owned by the Starnes family 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 of S 3°F. Mrs Starnes suspects that the manufacturer is overstating how well the thermostat works.

Short answer

standard deviation = $3^o$F as per null hypothesis

standard deviation is greater than $3^o$F as per alternative hypothesis.

Step-by-step solution

introduction

Given,

The temperatures at the Colorado cabin owned by the Starnes family can stay well below freezing for weeks at a time.

The standard deviation claimed by the manufacturer is $3^o$F

explanation

Calculating the null and alternative hypotheses,

standard deviation $\sigma$= $3^o$F as per null hypothesis

$\Rightarrow H_0:\sigma =3$

standard deviation is greater than $3^o$F as per alternative hypothesis.

$\Rightarrow H_a:\sigma >3$

The standard deviation is $3^o$F as per null hypothesis and standard deviation is greater than$3^o$ F as per alternative hypothesis.