The following table shows the results from a random sample data of 50 people on the relationship between dietary preference and athletic status.Dietary Preference Athletic Status Vegetarian Non-Vegetarian Row TotalAthlete 13 15 28Non-Athlete 8 14 22Column Total 21 29 50Using the information in the table, compute the expected frequencies for each of the cells in the table.Expected Frequencies for Dietary Preference Athletic Status Vegetarian Non-Vegetarian Row TotalAthlete 28Non-Athlete 22Column Total 21 29 50
Question
The following table shows the results from a random sample data of 50 people on the relationship between dietary preference and athletic status.Dietary Preference Athletic Status Vegetarian Non-Vegetarian Row TotalAthlete 13 15 28Non-Athlete 8 14 22Column Total 21 29 50Using the information in the table, compute the expected frequencies for each of the cells in the table.Expected Frequencies for Dietary Preference Athletic Status Vegetarian Non-Vegetarian Row TotalAthlete 28Non-Athlete 22Column Total 21 29 50
Solution
To calculate the expected frequencies for each cell in the table, we use the formula:
Expected frequency = (Row total * Column total) / Grand total
Let's calculate for each cell:
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Athlete and Vegetarian: Expected frequency = (28 * 21) / 50 = 11.76
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Athlete and Non-Vegetarian: Expected frequency = (28 * 29) / 50 = 16.24
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Non-Athlete and Vegetarian: Expected frequency = (22 * 21) / 50 = 9.24
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Non-Athlete and Non-Vegetarian: Expected frequency = (22 * 29) / 50 = 12.76
So, the table of expected frequencies would look like this:
Expected Frequencies for Dietary Preference Athletic Status Vegetarian Non-Vegetarian Row Total Athlete 11.76 16.24 28 Non-Athlete 9.24 12.76 22 Column Total 21 29 50
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