ISDS 361A-37_Chew

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Pennsylvania’s Average Gas Price 1 Pennsylvania’s Average Price of Regular Gasoline Esther Chew Business Department, California State University - Fullerton ISDS 361A - 37 Business Analytics I Professor Zhang December 3, 2023

Pennsylvania’s Average Gas Price 2 Introduction This report’s purpose is to evaluate the results of AAA’s report on average regular gasoline prices in Pennsylvania and analyze the randomly selected data. Statistical methods are used in descriptive statistics and the interval estimation to construct and analyze the figures in box plot and the confidence interval. Problem AAA reported during Memorial Day weekend in 2010 that the average price of regular gasoline was $2.65 per gallon. The following data show the price per gallon of regular gasoline for 15 randomly selected stations in the state. Description of Data Mean Price The mean will need to be calculated by SUM (all prices)/sample size. This translates to 39.62/15 = 2.64. This data shows that the average value per gallon of regular gasoline for 15 selected stations chosen at random in Pennsylvania. The upper and lower limits $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

Pennsylvania’s Average Gas Price 3 To calculate the upper and lower limits of the box-plot, we need to find the Q1, first quartile, and Q3, third quartile, and the IQR, interquartile range. Going off the data table shown, Q1 is 2.58 and Q3 is 2.73. To calculate the IQR we will need to follow the equation: Q3 - Q1, using the data that would equal to 0.15. The lower limit = Q1 - 1.5(IQR) = 2.36 and the upper limit = Q3 + 1.5(IQR) = 2.96. These two values, lower and upper limit, represent the two smallest and the two largest values of the box-plot. According to the data, the upper and lower limit indicate the lowest and highest gas prices used by gas stations. Any price that goes beyond these two limits would be considered outliers. Outliers are observations that lie outside the normal distance from other values in a random sample (NIST). After reviewing the data, there are no numbers that are lower than 2.36, or higher than 2.96. This tells us that no gas station uses a higher price level than others. Construction the 95% confidence interval In order to construct the 95% confidence interval the following formula will need to be used: Mean ± Margin of Error. After using excel, the standard deviation (s) = 0.09, critical value (t) = -2.14, and MOE = t x s/ √ n = -0.05. The interval estimation is then calculated: (2.64 - 0.05, 2.64 + 0.05) which equals (2.59, 2.69). After analyzing the data, we are 95% confident that the average price of gallon of gas in Pennsylvania during Memorial Day weekend in 2010 is around $2.59 to $2.69. Analysis

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Pennsylvania’s Average Gas Price 4 After analyzing both the box-plot and confidence interval, it shows us the overview of the data table. The value ranges with their correlating percentages like middle 50% of gas prices will fall between the range of $2.58 and $2.73 for box-plot. 95% of the average gas price will be between the range of $2.59 and $2.69. Only limited indicators are shown in the box-plot, on the other hand, data from the confidence interval estimates the value of the population. Conclusion A hypothesis regarding the reasonableness of the results given by AAA has been made. The average cost of regular gasoline in Pennsylvania over Memorial Day weekend in 2010 was $2.65 per gallon, according to AAA. This price falls within the previously analyzed range of $2.59 to $2.69, meaning that the AAA's reported results are statistically defensible.

Pennsylvania’s Average Gas Price 5 Reference National Institute of Standards and Technology. What are outliers in the data?. 7.1.6. what are outliers in the data? https://www.itl.nist.gov/div898/handbook/prc/section1/prc16.htm

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