Statistics with Aviation Application

Statistics with zephyr ApplicationChristopher WrightA. Type ofstatistical testyou planto conduct(check one, and giverelevant elaborate) 1-sample t-testa) Target populationb) investigate variablec) Research questiond) Expected settlement matched pairs t-testa) Target population(s)b) The research variable pass on be the difference betwixt andc) Research questiond) Expected result 2-sample t-testa) Target populations (2) Total become measure amidst Midway and capital of Colorado Houston and capital of Colorado b) Research variable Average tot up motivity era c) Research question Is the fair tally rifle judgment of conviction flitting into Denver from Midway and Houston the homogeneous?d) Expected result The average total get off age is non the aforesaid(prenominal).B. Data collection plan(check one,and give relevant enlarge) I forget use selective information from a file. Give pick up of file and details below.I leave alone be using the sou-west Airline Data fou nd in StatCrunch to test my hypothesis.I allow for obtain information from a website(s). Give Name of website(s), full URLs and details below. Other data collection plan Give specific details below.Project plan is NOT Accepted x AcceptedDate 3/2/17 Instructor Initials SHIntroduction The intent of this t-Test brook is to meditate and get wind the average total travel times between Midway external airport (MDW) and Denver International airport ( hideaway) William P. Hobby airport (HOU) and Denver International airport (DEN). Geographically speaking, both streets travel nearly the same maintain with the final destination being DEN. This begs the question, is the average total travel time flying into DEN from MDW and HOU the same? To test this question, this paper allow review a random sample of travel times between both routes of travel. Common sense tells us that counterbalance though the maintain traveled to DEN for both routes is nearly the same, there argon separate va riables (ex. ground delays, maintenance and weather) that croupe affect the total travel time of an aircraft. Therefore, the hypothesis will be that the average total travel time between the two routes will not be the same.This con postr will save be discussing all southwestward Airline flight of stepss departing from MDW and HOU traveling to DEN. A random sample of 50 routes will be calm and tested. The concentrate variable will be the average total travel time between the two respective locations and will be collected and cypher in minutes.It is important to note that the result of this test will only be valid indoors the test parameters.(Source ForeFlight)Study DesignThe study will be conducted as a two-sample t-Test with a 95% agency musical interval and a 0.05 level of significance.HypothesesH0 1 = 2 (MDW-DEN and HOU-DEN routes have the same mean travel time)Ha 1 2 (MDW-DEN and HOU-DEN routes do not have the same mean travel time)To test whether the total travel for both routes is the same, we will state that the null hypothesis is that the total travel time for both routes is the same. The alternative hypothesis will propose that the total travel time for both routes is not the same. The formulation of the hypothesis for this study will produce a two-tailed (left and right) result.DataThe data for this study was collected and is maintained by Embry-Riddle. It is located on the StatCrunch website under the MATH 211/222 data set group. The data that was collected was a sample of overall trading trading operations with Southwest Airlines at the Midway (MDW), Houston (HOU), and Dallas Love (DAL) airports. Southwest airlines operates from these airports almost both day and at multiple times during the day. For the sample to be substitute of the overall population, it would have to mimic these population parameters. The sample that was collected does rightful(prenominal) that. It is representative of the overall population of all Southwest Airl ine operations at MDW, HOU, and DAL because the data includes information from different days and times. This particular also lends itself to the avoidance of bias. The other key with avoiding bias is to be as random as possible while still representing the parameters of the overall population. Furthermore, for the purposes of this denomination we will assume that the appropriate steps were taken by Embry-Riddle to post its students that avoided bias to the best extent possible.From the large compilation of data, we will instantaneously shift the focus to the specific data to be tested. The data from prototype 1, located in the appendix, is the 50 specific data points that will be tested and includes the total travel times of both routes. To continue with readying for the t-Test, we will ensure that the samples are free and that the size is normal. The samples are independent because you can only be on one route of flight at a time, either traveling from MDW or HOU to DEN. Fi nally, for the purposes of this study will say that 50 data points (meeting the assignment requirement) is large enough, and therefore normal. work up 2 control 3Figure 4Figure 5Figure 6Figure 7Descriptive StatisticsAfter ensuring that the data meets all conditions required for our particular confidence level of 95%, it is important to severalise the data through statistical analysis and graphs (Figures 2 through 8). Figures 4 and 7 show that both sets of data have symmetrical distribution with little skew in either direction. Note thought that get in 4 displays Figure 8 a greater standard deviation. The boxplots ( strains 3 and 6) help better describe figures 2 and 5, but are more effectively displayed with a locating by side plotting as shown in figure 8. There we suck in that the medians are within 5 minutes of each other and that the data is not vastly separated. We can see that most of the data points from the HOU-DEN route would fit within the MDW-DEN IQR and that all of the HOU-DEN sample data would fit within the bounds of the min and max data points for MDW-DEN. This side by side comparison makes a strong argument that even through there are differences between the data of both routes, those differences may not be statically large enough to disavow the null hypotheses.FindingsOriginal Question Is the average total travel time flying into DEN from MDW and HOU the same?HypothesesH0 1 = 2 (MDW-DEN and HOU-DEN routes have the same mean travel time)Ha 1 2 (MDW-DEN and HOU-DEN routes do not have the same mean travel time)As we previously discussed, the initial look and plotting of the data showed that even though the routes were different, the data was close enough that it may not be statistically different enough to reject the null hypotheses. When looking at figure 10 and 11 to comparing the p-value (0.1627) to the significance level (0.05), we find that the p-value is big and therefore we do not reject the null hypothesis. This supports the expec ted findings and shows that even though the data between the two routes was slightly different, it was still not statistically different enough to reject the null hypothesis.In figure 9, the 95% confidence interval is 4.885 3.445, or about (-1.44, 8.33). This confidence interval includes 0 and therefore both the null and alternate hypothesis are plausible. Only after conducting the hypothesis test were we able to conclude not to reject the null hypothesis.Confidence Interval and Hypothesis Test Results Figure 9 Figure 10Figure 11Final handlingIn conclusion, we see that the average travel times between MDW and DEN HOU and DEN are very similar. So similar that we were unable to reject the alternative hypothesis that they were not the same. The results we obtained in the test were expected, especially considering that the distance traveled for each route is nearly the same. The biggest take away from this project is how close all of the data was for both routes. This shows just how accurate Southwest Airlines can be when it publishes the average times of travel for these routes, and also how effectively the can plan out their flying schedule. Specifically for the test conducted, we can see just how consistent their average flying time is between destinations separated by the same approximate distance.AppendixTotal sound Time SamplesMDW-DEN TimeHOU-DEN Time151154157149144140146141163136146cxxxv148143133134131135136132135135128142127141139146138138131148144153145144163146131165 one hundred fifty151147143144166149149148151Figure 1SourcesForeFlight. Vers. 8.2.3. N.p. ForeFlight, 2007-2017. computer software applicationStatCrunch. Computer software. www.statcrunch.com. Pearson Education, 2007-2017. Web. 6 Mar. 2017.Southwest Airline Data. StatCrunch Data analysis on the Web. Embry-Riddle aeronautic University, n.d. Web. 06 Mar. 2017. .