The national average for the price of a gallon of unleaded regular gas is $1.16. I believe the price is higher in my area of the country. I want to test my claim by randomly selecting gas prices for 25 stations in my area. The following prices are:
$1.27 $1.29 $1.16 $1.20 $1.37
1.20 1.23 1.19 1.20 1.24
1.16 1.07 1.27 1.09 1.35
1.15 1.23 1.14 1.05 1.35
1.21 1.14 1.14 1.07 1.10
The prices listed above are normally distributed. Using a one-sample t-test command and a level of significance of .05, state the five steps of the hypothesis testing procedure using:
a) non-directional hypothesis
b) directional hypothesis
*What should my recommendations be based on the hypothesis and the results?
*Are the decisions different in part a (non-directional) than in part b (directional)?
Explain why they would differ even if they don't?
* What are the tradeoffs of the two types of hypothesis?
This solution conducts an one-tailed and two-tailed small-sample test of hypothesis about a population mean. The null and alternative hypothesis is provided and the test statistic is calculated to determine if the null hypothesis is accepted or rejected.