Step 1 :The symbol for the random variable involved in this problem is \(X\).
Step 2 :The wording for the random variable in context is: 'The CO2 emissions for a random sample of 38 countries in 2010.'
Step 3 :The symbol for the parameter involved in this problem is \(\mu\), which represents the population mean.
Step 4 :The wording for the parameter in context is: 'The mean CO2 emission in 2004, which was 4.87 metric tons per capita.'
Step 5 :The null and alternative hypotheses are: \[\begin{array}{l} H_{0}: \mu = 4.87 \\ H_{A}: \mu \neq 4.87 \end{array}\]
Step 6 :A Type I error in the context of this problem would be concluding that the mean CO2 emission in 2010 is different from 4.87 metric tons per capita when it is actually the same.
Step 7 :A Type II error in the context of this problem would be failing to conclude that the mean CO2 emission in 2010 is different from 4.87 metric tons per capita when it is actually different.