Sample Responses Q6.pdf

The primary goals of Question 6 were to assess a student's ability to describe how sample data would differ using two different sampling methods, describe the sampling distribution of the sample mean for two different sampling methods, and choose the sampling method that will result in the best estimate of the population mean.

A sample obtained using Method 2 will not be representative of all tortillas made that day, as it only represents the tortillas from one production line. Method 1 was most likely used to select the sample, as the bimodal shape in the histogram of sample data indicates that tortillas were selected from both production lines.

Method 2 would result in less variability in the sample of 200 tortillas on a given day because the sample comes from only one production line. The sampling distribution of the sample mean diameter for samples obtained using Method 1 would be approximately normal with mean 6 inches and standard deviation 0.11/√200 inches.

Method 1 would result in less variability in the sample means over 365 days, as the sample means will all be very close to 6 inches. Method 1 is more likely to produce a sample mean close to 6 inches, as it results in less variability in the distribution of the sample mean.

The question is scored in three sections, with each section scored as essentially correct, partially correct, or incorrect. The scoring guidelines provide detailed criteria for each section, including the required components for an essentially correct response.