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Week 5: In class this week we've learned about hypothesis testing, and confidence intervals for two proportions. In this week's exercise, we will use a random sample of flights to compare two proportions. In particular, we'll ask if two airlines (Alaska and Southwest) have different market shares of flights from Portland (PDX). For this particular project, we'll make our lives easier with a contingency table. We'll treat this whole huge data set as if it were a random sample of all flights (it's not: why not?) *Open your data in Excel and answer (1) to (5) in complete sentences. To Begin: Build a Pivot Table. -Click on "Insert" then "Pivot Table" at the top left. (the default data range is great- the whole thing: 'Oregon Flight Data"!$A$1:... and New Worksheet). -On Pivot Table Fields on the right, choose ORIGIN and OP_UNIQUE_CARRIER. -Drag "ORIGIN" to Rows and "OP_Unique_Carrier" to columns. This should give you a blank table with airlines along the top and airports along the left. Then drag ORIGIN to values (and if necessary click on it to make it "Count of ORIGINS": for me that was the default and I didn't need to change anything. Your right hand pane "PivotTable Fields" should now look like this:PivotTable Fields Choose fields to add to report: Search D YEAR O QUARTER MONTH DAY_OF_MONTH DAY_OF_WEEK OFL_DATE OP UNIQUE CARRIER TAIL_NUM ORIGIN AIRPORT_JD ORIGIN ORIGIN_CITY_NAME ORIGIN STATE_ABR DEST_AIRPORT_JDDEST_CITY_NAME Drag fields between areas below T FILTERS I COLUMNS OP_UNIQUE_... ROWS E VALUES ORIGIN Count of ORI... and the top of your table should look like this:2 3 Count of ORIGIN Column Labels 4 Row Labels AA AS 86 DL F9 G4 HA NK OO UA WN Grand Total 5 ABQ 13 13 6 ANC 62 7 ATL 92 92 B AUS 31 31 you only really need the row for PDX (for me row 42). (1) What is the point estimate for the difference between the fraction of flights out of PDX run by Southwest (WN) and the flights out of PDX run by Alaska (AS)? Please show answer in a complete sentence and/or show your work. (2) What is the confidence interval for this distance (center +/-margin of error) for this difference. Please show your work (what terms you're multiplying/dividing) and answer in a complete sentence. (3) Compute a hypothesis test for the question: is there evidence of a difference between the market share of Alaska vs. Southwest. Write out the null and alternative hypotheses and level of significance alpha. (4) Calculate the test statistic and find the p-value. Please show your work. (5) Write your conclusion. This should both say whether or not you reject the null and say what this means in everyday language