A city council surveys residents and business owners about a proposed new public transportation system. The results of the survey are shown in the following 2 × 2 contingency table.
Which statement is true?
A.
A resident is slightly more likely than a business owner to favor the new transportation system.
B.
A resident is much less likely than a business owner to favor the new transportation system.
C.
A resident is slightly less likely than a business owner to favor the new transportation system.
D.
A resident is much more likely than a business owner to favor the new transportation system.
This question requires comparing conditional percentages from a two-way table. For residents, 150 out of 200 are in favor of the proposed transportation system. The resident support rate is therefore 150/200 = 0.75, or 75%. For business owners, 30 out of 100 are in favor. The business owner support rate is 30/100 = 0.30, or 30%. The difference is 75% − 30% = 45 percentage points, which is a large gap. Therefore, a resident is much more likely than a business owner to favor the new transportation system. Option A understates the magnitude of the difference by calling it slight. Options B and C reverse the direction of the comparison because residents have the higher support rate, not the lower one. The appropriate statistical tool here is conditional percentage because support is being compared within each respondent group. References/topics from the Study Guide: contingency tables, conditional percentages, two-variable categorical data, comparative proportions.
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