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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

A potato chip company produces the same number of snack-sized bags of potato chips every month. A manager at the company randomly selects a sample of snack-sized bags of potato chips to be weighed in a routine quality-assurance check each month. The January sample had a mean weight of 0.95 ounces and a margin of error of 0.06 ounces. The February sample had a mean weight of 0.98 ounces and a margin of error of 0.04 ounces. Based on these findings, which of the following is an appropriate conclusion?

A.Most of the snack-sized bags of potato chips produced by the company in January each had a weight of at least 0.95 ounces, while most of the snack-sized bags of potato chips produced by the company in February each had a weight of at least 0.98 ounces.
B.The mean weight of all the snack-sized bags of potato chips produced by the company in January must have been 0.03 ounces more than the mean weight of all the snack-sized bags of potato chips produced by the company in February.
C.The mean weight of all the snack-sized bags of potato chips produced by the company in January was 0.03 ounces less than the mean weight of all the snack-sized bags of potato chips produced by the company in February.
D.The number of snack-sized bags of potato chips in the January sample was less than the number of snack-sized bags of potato chips in the February sample.

答案和解析

答案：D

解析：

Choice D is correct. Start by interpreting the results of each sample individually before comparing the two.

The January sample had a mean weight of 0.95 ounces and a margin of error of 0.06 ounces. The February sample had a mean weight of 0.98 ounces and a margin of error of 0.04 ounces.

This means that the average weight of a snack-sized bag of potato chips in the January sample was less than the average weight of a snack-sized bag of potato chips in the February sample and that the margin of error for the January sample was larger than the margin of error for the February sample.

The weight of the samples does not mean that the entire populations had the same attributes, but the margin of error does give some insight about the sample sizes.
Since the population of all snack-sized bags of potato chips was the same in January as it was in February, the larger margin of error in January indicates that the January sample size was smaller than the February sample size.