Question at position 7 A large online retailer places packed and ready-to-be-shipped boxes in a line on a conveyor belt. A sample of boxes will be used to estimate the mean weight of boxes shipped on a given day. One proposed method for selecting the sample is as follows: Generate a random integer from 1 to 20. Use that integer to select an initial box from the first 20 boxes in line on the conveyor belt. Select ·every 25th box that follows the initial box on the conveyor belt for the rest of the day. Which of the following best describes the proposed sampling method? 4ST39A large online retailer places packed and ready-to-be-shipped boxes in a line on a conveyor belt. A sample of boxes will be used to estimate the mean weight of boxes shipped on a given day. One proposed method for selecting the sample is as follows: Generate a random integer from 1 to 20. Use that integer to select an initial box from the first 20 boxes in line on the conveyor belt. Select ·every 25th box that follows the initial box on the conveyor belt for the rest of the day. Which of the following best describes the proposed sampling method? 4ST39Convenience sampleSystematic random sample Stratified random sample, stratified by time of dayCluster sample, with times of day as clustersCluster sample, with box weights as clusters题目解析

Question

Question at position 7 A large online retailer places packed and ready-to-be-shipped boxes in a line on a conveyor belt. A sample of boxes will be used to estimate the mean weight of boxes shipped on a given day. One proposed method for selecting the sample is as follows: Generate a random integer from 1 to 20. Use that integer to select an initial box from the first 20 boxes in line on the conveyor belt. Select ·every 25th box that follows the initial box on the conveyor belt for the rest of the day. Which of the following best describes the proposed sampling method? 4ST39A large online retailer places packed and ready-to-be-shipped boxes in a line on a conveyor belt. A sample of boxes will be used to estimate the mean weight of boxes shipped on a given day. One proposed method for selecting the sample is as follows: Generate a random integer from 1 to 20. Use that integer to select an initial box from the first 20 boxes in line on the conveyor belt. Select ·every 25th box that follows the initial box on the conveyor belt for the rest of the day. Which of the following best describes the proposed sampling method? 4ST39Convenience sampleSystematic random sample Stratified random sample, stratified by time of dayCluster sample, with times of day as clustersCluster sample, with box weights as clusters题目解析

BlackTom AI · Accepted Answer

To begin, let's restate what the sampling method involves and the goal of the study. The scenario describes selecting a starting box at random from the first 20 boxes, then choosing every 25th box thereafter for the rest of the day in order to estimate the mean weight of boxes.
Option 1: Convenience sample. A convenience sample consists of selecting elements that are easiest to reach, not following a systematic rule or random start. Here, the method uses a random start and a fixed interval, so it is not merely based on ease of access. Therefore, this option is not describing the proposed method.
Option 2: Systematic random sample. In a systematic random sample, you pick a random starting point and then select members at regular intervals from the population list. The described process matches this pattern: a random start from the first 20 boxes, then every 25th box thereafter. This alignment with a fixed sampling interval after a random start is the hallmark of systematic sampling with a random start, making this a strong fit for the method.
Option 3: Stratified random sample, stratified by time of day. Stratified sampling would involve dividing the population into distinct subgroups (strata) and sampling from each subgroup, typically to ensure representation from each stratum. The description does not indicate any separation into time-of-day strata or deliberate sampling from multiple strata; it simply uses a single sequence with a random start. Hence, this is not a stratified sample.
Option 4: Cluster sample, with times of day as clusters. Cluster sampling would group units into clusters (here, possibly by time of day) and sample entire clusters or a subset of clusters. The procedure does not indicate sampling entire time-based clusters or selecting a subset of time blocks as clusters; it uses a continuous line with a fixed interval, so this label is not appropriate.
Option 5: Cluster sample, with box weights as clusters. This would imply clustering by weights themselves, which is not described and would not arise from taking every 25th box after a random start. The method does not create weight-based clusters, so this option mischaracterizes the approach.
In sum, the described procedure aligns with systematic sampling with a random start, rather than convenience, stratified, or cluster sampling. The key features are the random starting point and the fixed, regular interval used thereafter, which together define systematic random sampling. The remaining options fail to capture this structure for specific reasons.»

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