位置45的问题 A survey of 400 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school. [table]
| | | Undergraduate Major | | | | | | Graduate School | Business | Engineering | Other | Total | Yes | 35 | 42 | 63 | 140 | No | 91 | 104 | 65 | 260 | Total | 126 | 146 | 128 | 400
[/table] Of those students who are majoring in Business, what percentage plans to go to graduate school?72.22%8.75%70%27.78%

Question

位置45的问题 A survey of 400 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school. [table]
|  |  | Undergraduate Major |  |  |  |  |  | Graduate School | Business | Engineering | Other | Total | Yes | 35 | 42 | 63 | 140 | No | 91 | 104 | 65 | 260 | Total | 126 | 146 | 128 | 400
[/table] Of those students who are majoring in Business, what percentage plans to go to graduate school?72.22%8.75%70%27.78%

BlackTom AI · Accepted Answer

Question restatement: A survey of 400 college seniors produced a crosstab of Undergraduate Major (Business, Engineering, Other) by whether they plan to go to Graduate School (Yes, No). Of those students who are majoring in Business, what percentage plans to go to graduate school?
Options provided: 72.22%, 8.75%, 70%, 27.78%

Now, evaluate each option in light of the data shown.

Option A: 72.22%
To assess this, look at the Business row under Yes and Total. The number planning to go to graduate school among Business majors is 35, and the total number of Business majors is 126. The percentage is 35/126. 35 divided by 126 equals approximately 0.2778, which is 27.78%. Therefore, 72.22% would correspond to 91/126, which is not the correct proportion for Yes out of Total. This option misinterprets the distribution and overstates the Yes proportion.

Option B: 8.75%
This percentage would imply a very small fraction of Business majors plan to go to graduate school. If we compute 8.75% of the Business total (126), that would be about 11.0 students. The actual count for Yes in Business is 35, not 11, so this option does not match the observed data and is incorrect.

Option C: 70%
A 70% figure would correspond to roughly 88.2 students out of 126, which is not aligned with the observed Yes count of 35. Since 35/126 is about 27.78%, this option greatly overestimates the proportion and cannot be correct based on the data.

Option D: 27.78%
This uses the Yes count (35) divided by the Business total (126). 35 ÷ 126 = 0.277777..., which converts to 27.78%. This exactly matches the data given for the Business major row and the Yes column, correctly representing the fraction of Business majors who plan to go to graduate school.

Summary of reasoning across options: The correct computation hinges on the Business row totals: Yes = 35, Total = 126, giving 35/126 = 0.2778 = 27.78%. Options A, B, and C derive from miscounting, misplacing the numerator, misinterpreting the denominator, or using an incorrect proportion, leading to results of 72.22%, 8.75%, and 70% respectively. The key is to divide the number of Business majors who said Yes by the total number of Business majors and convert to a percentage, which yields 27.78%.

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