Finding Expected Frequencies
In Exercis...

Question

Finding Expected Frequencies

In Exercises 7–12, (a) calculate the marginal frequencies and (b) find the expected frequency for each cell in the contingency table. Assume that the variables are independent.

Contingency table showing movie rental frequency by age group and genre: Comedy, Action, and Drama.

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Calculate the marginal frequencies for the following contingency table and find the expected frequency for each cell assuming independence. Group 1, group 2, Type A, 1525, Type B 1020. Awesome. So it appears for this particular problem we're asked to solve for 3 separate answers. We're asked to calculate the marginal frequencies for the following contingency table, and we're asked to find the frequency for each cell assuming independence. So that means we need to figure out what the, what the row totals are, what the column totals are, and what the expected frequencies are, and those are the final three answers that we're trying to solve for. So with that in mind, Our first step that we need to take we need to add the row total. So when we add the row totals, we will find that for group one, which I'll just call 1 for short, we need to take 15. Plus 10, which will give us an answer of 25. And for group 2, which I'll just call 2, we need to take 25 plus 20, which will give us an answer of 45. And for our second step, we need to add the column totals for type A, which I'll just call A for short, we need to add 15 + 25, which will give us an answer of 40. And for type B, which I'll just call B, we need to take 10 + 20, which will give us an answer of 30. Our third step now is we need to find the grand total, so we need to add all of our values together, so we need to take 15 + 10 + 25 plus 20, which will give us an answer of 70. Our fourth step now is we need to calculate the expected frequencies for each cell. So for group 1, type A, plugging in our known data, we need to take 25 multiplied by 40 divided by 70, which will give us an answer when we plug into our calculator and round to the nearest full number of 14. So for our first condition, which is group 1, type A, It's approximately equal to 14. So for group one, type B condition, we need to take 25 multiplied by 30 divided by 70, and this will be approximately equal to 11 when we round to the nearest whole number. And for the condition group 2, type A, We need to take 45 multiplied by 40 divided by 70, which will give us an answer of approximately 26 when we round to the nearest whole number. And finally, for the condition group 2 type B, we need to plug in 45 multiplied by 30 divided by 70, which when you plug that into our calculator and we round to the nearest full number, we will find that it's approximately equal to 19. So with that in mind, our final answers for me. But when we collect all of our data and we put it into one place to organize our answers, you will find that our final answers without a doubt, are going to be the following. The row totals are 25 and 45, the column totals are 40 and 30, and the expected frequencies are 1411, 26, and 19. And that's it. Those are our final answers. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Finding Expected Frequencies
In Exercises 7–12, (a) calculate the marginal frequencies and (b) find the expected frequency for each cell in the contingency table. Assume that the variables are independent.

Key Concepts

Marginal Frequencies

Expected Frequencies

Independence of Variables

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