A research manager selected $2$ random samples of ovens of a certain …

Question

Prompt

A 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

35 0^{\circ} F

. The research manager recorded the amount of time, in minutes, each oven takes to preheat to

35 0^{\circ} 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

35 0^{\circ} 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

35 0^{\circ} 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?

The first sample contained fewer ovens than the second sample.

The first sample contained more ovens than the second sample.

The first sample took less time on average to preheat to

35 0^{\circ} F

than the second sample.

The first sample took more time on average to preheat to

35 0^{\circ} F

than the second sample.