Hypothesis Testing (Gas Prices) Essay

1103 words - 4 pages

In the last study, Team C compared the national gas price average as reported by AAA.com to various gas prices in different cities in the Eastern US. Taking the study a step further, Team C elected to test the gas prices in two states, Florida and Michigan, to further research such prices. After further research, results reported that the gas averages in Florida and Michigan were calculated at $2.60 and $2.61, respectively. Team C decided to take this a step further and determine if the $.01 difference could be tested as an accepted hypothesis that the gas prices in Florida are in fact cheaper by one penny rather than a null hypothesis that prices in the two states are the same.ProcedureAs in any hypothesis test, the procedure begins by identifying null and alternate hypothesis statements. Next, Team C determines the level of significance or probability of rejecting the null hypothesis when it is true (Lind, Marchal, and Wathen 2004). The third step is selecting a test statistic or value from the sample. A decision rule formulates, which will determine acceptance or rejection of the null hypothesis. Finally, Team C compares the test statistic to the critical value and reports the results. Team C's sample consists of 20 gas stations from Florida and Michigan, (Appendix A).Identification of Hypothesis:Ho: umichigan >= ufloridaH1: umichigan < ufloridaµ 1 - Michigan = 2.61µ 2 - Florida = 2.60Sample Size 10 of each groupTeam C's sample of gasoline prices in the two states was taken from 20 gas stations (Appendix A). The team generated data from randomly selected stations via drive-by analysis and data from msnautos.com. The samples were drawn from various gas stations, some of which included Shell, BP, Chevron, and Mobil. As stated above, the mean gas price in the Florida was reported by Team C at $2.60 and the mean price in Michigan was $2.61.Level of SignificanceAlpha is also known as the level of significance. Note that alpha is the confidence interval, which is "the range of values within which we expect the population parameter to occur" (Lind, Marchal, Wathen 2004). Therefore, a level of significance of .05 corresponds to 95%. Once again Team C chose a five percent significance level because this is the standard level used for consumer research projects. This level of significance describes the risk the test is taking of rejecting the null hypothesis when it is true, (Lind, Marchal, Wathen 2004). Five percent describes the area under the normal distribution curve that results in the rejection of the null hypothesis.Test StatisticWhen choosing a test statistic for a hypothesis test, it is important to consider a few guidelines about the sample. The first is whether or not the sample follows a normal distribution. In order to use the z or t- statistic, it must be assumed that the data follows a standard normal distribution. The second consideration is the size of the sample when choosing a test statistic. For sample sizes less...

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