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In a 2012 report from the U.S. Department of Education breaking down the race and gender of every U.S. college graduate receiving a bachelor's degree in 2009–2010, we see the following data for white, black, and Hispanic graduates. (Numbers are in 1000s.)GenderRace Males Females BothWhite (Expected) 514 (508.32) 654 (689.68) 1198Black (Expected) 56 (70.01) 109 (94.99) 165Hispanic (Expected) 55 (59.40) 85 (80.60) 140Total 625 848 1473Source: “Degrees Conferred by Sex and Race,” National Center for Education Statistics, U.S. Department of Education. https://nces.ed.gov/fastfacts/display.asp?id=72What is the chi-squared statistic for this data? 3.81 6.63 2.80 2.06

Question

In a 2012 report from the U.S. Department of Education breaking down the race and gender of every U.S. college graduate receiving a bachelor's degree in 2009–2010, we see the following data for white, black, and Hispanic graduates. (Numbers are in 1000s.)GenderRace Males Females BothWhite (Expected) 514 (508.32) 654 (689.68) 1198Black (Expected) 56 (70.01) 109 (94.99) 165Hispanic (Expected) 55 (59.40) 85 (80.60) 140Total 625 848 1473Source: “Degrees Conferred by Sex and Race,” National Center for Education Statistics, U.S. Department of Education. https://nces.ed.gov/fastfacts/display.asp?id=72What is the chi-squared statistic for this data? 3.81 6.63 2.80 2.06

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Solution

To calculate the chi-squared statistic for this data, we need to use the formula:

χ² = Σ [ (O-E)² / E ]

where:

  • O is the observed frequency (the actual data from the study)
  • E is the expected frequency (what we would expect to see if there was no effect)

For each cell in the table, we subtract the expected frequency from the observed frequency, square the result, and then divide by the expected frequency. We then sum all of these values to get the chi-squared statistic.

Let's calculate:

For White Males: (514 - 508.32)² / 508.32 = 0.062

For White Females: (654 - 689.68)² / 689.68 = 0.186

For Black Males: (56 - 70.01)² / 70.01 = 2.82

For Black Females: (109 - 94.99)² / 94.99 = 2.09

For Hispanic Males: (55 - 59.40)² / 59.40 = 0.33

For Hispanic Females: (85 - 80.60)² / 80.60 = 0.24

Adding these all together gives us the chi-squared statistic:

0.062 + 0.186 + 2.82 + 2.09 + 0.33 + 0.24 = 5.73

So, the chi-squared statistic for this data is 5.73. This is not one of the options given in the question. Please check the data or the options again.

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