Interpret our confidence interval in the context of the study.

Question

BlackTom AI · Accepted Answer

First, let's restate the scenario to be clear: the question asks us to interpret the confidence interval in the study comparing standardized prices between 0.99 carat and 1 carat diamonds, and we must evaluate each stated interpretation.
Option A: 'We are 95% confident that the average standardized price of a 0.99 carat diamond is $3.27 lower to $21.33 higher than the average standardized price of a 1 carat diamond.' This wording claims the interval spans from a $3.27 decrease to a $21.33 increase. The directionality here implies that the 0.99ct price could be either lower or higher than the 1ct price within those bounds, which is inconsistent with the given answer text that specifies the interval is entirely lower (i.e., the 0.99ct price is lower than the 1ct price). Therefore, as stated, this option mixes a lower bound with an upper bound in the wrong directional sense and is not aligned with the correct interval.
Option B: 'We are 95% confident that the average standardized price of a 0.99 carat diamond is $3.27 to $21.33 lower than the average standardized price of a 1 carat diamond.' This option states a lower bound of $3.27 and an upper bound of $21.33, both described as decreases relative to the 1 carat price. The key here is that both endpoints describe how much cheaper the 0.99ct diamond is, which matches the intended interpretation of the interval that the 0.99ct price is lower than the 1ct price by an amount in that range. The phrase 'to' indicates the interval spans from a smaller decrease to a larger decrease, which correctly reflects a one-sided comparison (0.99ct vs 1ct) with the entire interval indicating lower prices. This interpretation is consistent with the provided correct answer text.
Option C: 'We are 95% confident that the average standardized price of a 0.99 carat diamond is $21.33 lower to $3.27 higher than the average standardized price of a 1 carat diamond.' Here the order of the bounds is reversed: it starts with a larger decrease ($21.33 lower) and ends with a higher amount ($3.27 higher). Moreover, mixing a drop and a rise within the same interval contradicts the idea of a unidirectional interval for the difference in means. This option misstates both the direction and the ordering of the bounds, making it inconsistent with the correct interpretation.
Option D: 'We are 95% confident that the average standardized price of a 0.99 carat diamond is $3.27 to $21.33 higher than the average standardized price of a 1 carat diamond.' This option claims the 0.99ct price could be higher than the 1ct price by as much as $21.33, which directly contradicts the provided context that the 0.99ct price is lower. Since the comparison should show the 0.99ct price being lower, this option states the opposite relationship and is therefore incorrect.

To summarize the reasoning, option B correctly represents a confidence interval describing how much cheaper (lower) the 0.99 carat price is relative to the 1 carat price, with bounds that both indicate decreases. The other options either reverse the direction, misstate the bounds, or imply the 0.99ct price could be higher, which conflicts with the correct interpretation.

FA25_QTM_100_3 7.26: Diamonds, Part II. - Requires Respondus LockDown Browser

Interpret our confidence interval in the context of the study.

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