A Bloomberg BusinessWeek subscriber study asked, "In the past 12 months, when traveling for busi

1. First, we need to find the expected frequencies for each cell in the table. To do this, we mu

A Bloomberg BusinessWeek subscriber study asked, "In the...

A Bloomberg BusinessWeek subscriber study asked, "In the past 12 months, when traveling for business, what type of airline ticket did you purchase most often?" asked if the type of airline ticket purchased most often was for domestic or international travel. Sample data obtained are shown in the following table. Type of Flight Type of Ticket Domestic International First Class 21 26 Business Class 122 96 Economy Class 132 518 a. Using a .05 level of significance, is the type of ticket purchased independent of the type of flight? Use Table 12.4. H0: Type of ticket purchased is independent of the type of flight Ha: Type of ticket purchased is not independent of the type of flight Compute the value of the ?2 test statistic (to 2 decimals).

Transcript

00:01 Alright, in your question, you're working on a kai squared test of independence.

00:05 You're given this table, you've already selected the appropriate hypothesis for your null and alternative.

00:13 And we need to calculate the kai squared statistic.

00:17 So what we first want to do is i added a total row and a total column to this table.

00:25 I want to add up the domestic flights, which works up to 275.

00:31 I want to add up the international, which is 640.

00:35 Then we have our total of 915.

00:38 Now i want to add the rows, which would be 47, and the next one would be 218, and the next one would be 650.

00:55 And i'm going to figure out, okay, what percent should have selected first class for each flight.

01:07 So looking at this total, i want to figure out what these percentages are, and then i'll use that in my next step.

01:19 So i'm just doing 47 divided by 915.

01:24 It's probably not going to be a nice decimal.

01:27 It's not.

01:27 So i'm going to leave it 47 over 915.

01:32 This one would be 218 over 915.

01:36 And this would be 650 out of 915.

01:41 Again, those represent basically what we should expect the distribution to be for first class, business class, and economy class.

01:50 And now we'll multiply it to the total for domestic flights.

01:55 So i'm going to take each of these times 275 to get an expected value, which i'll put in parentheses, beside each domestic number.

02:09 So i'm going 47 divided by 915 times 27.

02:16 Which would give me 14 .1257.

02:23 I'm going to round it to four decimal places for the expected amount of domestic passengers that would travel first class.

02:31 Now i'll do 218 divided by 915 times 275, and that would be 65 .5 .591.

02:49 And then the next one would be 132.

02:56 I'm sorry, not 132...

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