Gas Prices Iowa City vs Cedar Rapids Group Members Kevin Kaiser Michael Bries Statistical Methods and Computing 22S 30 Prof Kate Cowles 1 Introduction In the classic high school days comedy Dazed and Confused there is a scene that shows several of the characters pulling up to a gas station to pick up a few beverages to get their evening started off right The camera follows the Dodge Charger into the lot and pulls off to get a full view of the station As two of the teenagers walk into the station the audience is given a shot of the station marquee The most poignant aspect of this particular sign is the price upon it In the year this movie is set gas sold for a price of 0 37 per gallon Prices since that time have increased over 5 fold keeping well ahead of the pace of inflation There are many factors that affect the price of the gas we buy to power our vehicles aircraft ships and trains Just like any product on the market today oil falls under the economic rules of supply and demand More and more people in this country and around the world are driving As the quantity of oil demanded increases the market will naturally increase its price to accommodate In 2003 total oil production across the globe reached 68 million barrels per day with most of that production coming from Middle East countries The Organization of Petroleum Exporting Countries OPEC was formed in 1960 to regulate the trade of petroleum from some of the largest oil producing countries OPEC can single handedly raise and lower gas prices simply by dictating how much petroleum they will produce OPEC is probably the most powerful organization in the world today and will continue to be a mover and shaker as long as countries such as the U S have such a great demand for their product Aside from the Saudi Arabias and the Irans of the world there are many other small factors that affect the price we pay The factor we decided to study was simple geography Iowa City and Cedar Rapids are separated by less than 20 miles One would think there would be almost no difference in prices considering transportation costs from one to the other would be minimal As the price nudges ever more closely to the 2 point we decided to see if there was any significant difference in gas prices between the two main cities of Iowa s Technology Corridor 2 Data Collection Method In order to secure a simple random sample for the prices it was important to collect data from multiple areas and many different stations Twelve to fifteen stations was determined to be a large enough sample size to ensure normality of the sample Stations in Iowa City were chosen sporadically from northern stations near Interstate 80 to southerly stations along Highways 1 and 6 Stations in Cedar Rapids varied from those close in proximity to Interstate 380 to downtown stations along First Avenue all the way out to stations near Marion Both regions covered an area large enough to provide randomness to the sample Data was collected on Tuesday April 13 2004 Initially the study was stratified to collect data on three different days including a day during the weekend However since the sample size was large enough it was decided to just choose only one day to collect the data 3 Price Data Analysis In order to compare the gas prices between Iowa City and Cedar Rapids we decided to use two different tests a two independent sample t test and a Wilcoxon Rank Sum test The first test we used was a two independent sample t test We chose a two independent sample t test over a paired sample t test because we wanted to compare the mean gas price from two different populations gas stations in Iowa City and gas stations in Cedar Rapids The variable of interest was the price gallon of gas Table 1 shows the sample data that we collected from the two different cities Observation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Gas Price Cedar Rapids Iowa City 1 739 1 779 1 669 1 769 1 649 1 779 1 669 1 759 1 629 1 759 1 669 1 779 1 789 1 779 1 679 1 759 1 679 1 859 1 499 1 759 1 699 1 789 1 719 1 759 1 769 1 779 1 679 1 779 1 769 1 760 Table 1 Sample data There are a few assumptions that have to be made when comparing means from two populations 1 2 3 4 5 We have two simple random samples from two distinct populations The samples are independent The sizes of the two samples need not be the same We measure the same variable for both samples The populations are normally distributed It is very important that these assumptions are met in order for the integrity of the test to be upheld Assumption one was met because the samples that we took were from two distinct populations Iowa City gas stations and Cedar Rapids gas stations In addition the samples we took were simple random samples because we randomly took samples from all over the two different cities In Iowa City for example we didn t only take samples from the downtown area we took samples from all over the entire city The two samples are independent because the selection of one sample has no influence on the selection of the other there is no matching We measured the same variable for both of the samples price gallon of gas To verify that the fifth assumption is met we have to take a look at the stemplots and boxplots of the data collected Figure 1 shows the stemplot and boxplot of the Iowa City data As you can see the data is slightly skewed to the right and there is one outlier However since the sample size is relatively large n 15 it doesn t matter that it is skewed because tprocedures are quite robust against violations of normality assumptions especially when the sample sizes are the same As lecture 19 states t procedures are quite accurate even for n1 n2 as small as 5 Therefore we can assume that assumption five is met Stem Leaf 184 9 1 182 180 178 9 1 176 09999999 8 174 99999 5 Multiply Stem Leaf by 10 2 Boxplot Figure 1 Iowa City gas prices Figure 2 is the stemplot and boxplot of the Cedar Rapids data As can be seen from the plot there is one outlier in the Cedar Rapids data However the data is relatively normal so we can assume that the Cedar Rapids gas stations population is normally distributed The presence of outliers in our sample data does cause a little bit of a concern but since all assumptions were met a two sample t test was carried out to analyze our data Stem Leaf 17 779 3 17 024 3 16 5777888 7 16 3 1 15 15 …