Question

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 1. 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 10 randomly selected pieces of a particular type of glass: 11 1.07 1.1 .07 1.12 1.08 1.18 108 1.12 1.08 Use a 0.05 significance level to test the claim that the average conductivity of this type of glass is greater than 1. Write your code in R Markdown and write your null and alternative hypotheses, and your decision as a comment in your R Markdown file.

Answer 1

R code-

X=c(1.1,1.07,1.1,1.07,1.12,1.08,1.18,1.08,1.12,1.08)
t.test(X,mu=1, alternative=c("greater"))

Output-

        One Sample t-test

data:  X
t = 9.3934, df = 9, p-value = 3.004e-06
Null hypothesis: mean is 1
alternative hypothesis: true mean is greater than 1

As p-value is less than alpha=0.05 so we reject the null hypothesis. Therefore we have sufficient evidence to conclude that the average conductivity of this type of glass is greater than 1