Use the following example to explain this question, why do you only need to calculate a critical value for a simple hypothesis i.e. μ = c, even if your null is μ ≥ c or μ<= c?
An engineering research center claims that, through the use of a new computer control system, automobiles should achieve, on average, at least an additional 5 miles per gallon of gas. A random sample of 81 automobiles was used to evaluate this product. The sample mean increase in miles per gallon achieved was 4.5, and the sample standard deviation was 2.9 miles per gallon.
State the appropriate null and alternative hypotheses and answer the question.