The question is as follows:

AAA reported that the average price of regular gasoline in Pennsylvania during Memorial Day weekend in 2010 was $2.65 per gallon. The following data show the price per gallon of regular gasoline for 15 randomly selected stations in the state.

$2.73 $2.59 $2.74 $2.65 $2.71

$2.73 $2.51 $2.71 $2.61 $2.64

$2.58 $2.46 $2.64 $2.74 $2.58

Your report should include the following sections:

1. Title page
2. Introduction and problem background
3. Data description
   • Calculate the mean - show your calculations. Give an explanation as to what this means in relation to this problem.
   • Calculate the standard deviation - show your calculations. Give an explanation as to what this means in relation to this problem.
   • Provide an image of the box-plot of the data.
   • Calculate the median - show your calculations. Give an explanation as to what this means in relation to this problem.
   • Calculate the first and third quartiles - show your calculations. Give an explanation as to what this means in relation to this problem.
   • Calculate the upper and lower limits of the box-plot - show your calculations. Give an explanation as to what this means in relation to this problem.
   • Construct the 95% confidence interval to 4 decimal places (make sure to include whether you used z or t) - show your calculations. Give an explanation as to what this means in relation to this problem.
   • Perform the appropriate hypothesis test. Be sure to state your significance level, test statistic, and p-value (make sure to include whether you used z or t) - show your calculations. Give an explanation as to what this means in relation to this problem.
4. Analyses
   • Describe the skewness of the data.
   • Describe the similarities and differences between the box plot and confidence interval calculated.
   • State the conclusion of your hypothesis test.
5. Interpretation of results and conclusion
   • Do your confidence interval and hypothesis test agree? Explain.
   • Do the results from the sample validate AAA 's findings that the average price of gasoline was $ 2.65 per gallon? Explain.