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Math·Problem-Solving and Data Analysis·Inference from sample statistics and margin of error
mediumA research manager selected 2 random samples of ovens of a certain type to estimate the average amount of time this type of oven takes to preheat to 350 degrees Fahrenheit (∘F). The research manager recorded the amount of time, in minutes, each oven takes to preheat to 350∘F. Based on the first sample, the research manager estimated that this type of oven takes an average of 14.2 minutes to preheat to 350∘F, with an associated margin of error of 1 minute. Based on the second sample, the research manager estimated that this type of oven takes an average of 14.4 minutes to preheat to 350∘F, with an associated margin of error of 2.2 minutes. Assuming the margins of error were calculated the same way, which of the following best explains why the first sample obtained a smaller margin of error than the second sample?
A
The first sample contained fewer ovens than the second sample.
B
The first sample contained more ovens than the second sample.
C
The first sample took less time on average to preheat to 350∘F than the second sample.
D
The first sample took more time on average to preheat to 350∘F than the second sample.