Q. 72 - The Practice of Statistics for AP

Question

Heat through the glass How well materials conduct heat matters when designing houses, for example. Conductivity is measured in terms of watts of heat power transmitted per square meter of surface per degree Celsius of temperature difference on the two sides of the material. In these units, glass has conductivity about $1$. The National Institute of Standards and Technology provides exact data on properties of materials. Here are measurements of the heat conductivity of $11$ randomly selected pieces of a particular type of glass:

$1.11 1.07 1.11 1.07 1.12 1.08 1.08 1.18 1.18 1.18 1.12$

Is there convincing evidence that the conductivity of this type of glass is greater than $1$? Carry out a test to help you answer this question.

Step-by-Step Solution

Answer

There is no convincing evidence that the conductivity of this type of glass is greater than $1$ .

Step 1: Given information

The National Institute of Standards and Technology provides exact data on properties of materials. Here are measurements of the heat conductivity of $11$ randomly selected pieces of a particular type of glass:

$1.11 1.07 1.11 1.07 1.12 1.08 1.08 1.18 1.18 1.18 1.12$

Step 2: Explanation

State: $H_0:\mu =1\text{ versus }{H}_a:\mu >1$, where $\mu$ is the actual mean amount of thermal conductivity

Plan: One-sample t test for $\mu$.

Random: The sample was randomly selected. 

Normal: Previous experience tells us that thermal conductivity will be close to Normal. Independent: There are at least $11$ selected glasses. 

Do: $t = 9.95$, $P-value = 0$.

Conclude: Since our P-value is less than $0.05$, we reject $H_0$.

There is no convincing evidence that the conductivity of this type of glass is greater than$1$.