Student researchers wanted to determine a person’s ability to estimate the number of beans in a bag. They had 1,470 beans in a clear bag for the subjects to estimate. They also showed the subjects another clear bag that contained 200 beans and told them the number in that bag. They thought this would help them estimate the number of beans in the larger bag. The 40 subjects were a representative sample of the students at the researchers’ school. The subjects’ estimates are shown in the dotplot. The mean estimate is 962.9 beans and the standard deviation is 351.7 beans.

a. Describe the parameter estimated by the students. 

b. Verify the validity conditions for a theory-based confidence interval. 

c. Use the Theory-Based Inference applet to construct a 95% confidence interval and interpret it in the context of the problem. 

d. Based on your confidence interval do you have strong evidence that, on average, students cannot accurately estimate the number of beans in the bag? Explain.

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400 800 : 1200 Estimate (number of beans) 1600 2000