Carlos and Dana each inspected 200200 manufactured widgets for defects. Carlos found 1212 defective widgets and Dana found 99 defective widgets. Which explanation best accounts for the difference between their estimated defect rates?

The difference is significant because 0.0150.015 is greater than both individual standard errors, proving a real difference.

The estimates differ due to a calculation mistake since with 200200 observations such a difference cannot occur by chance.

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Problem 153Multiple Choice

Carlos and Dana each inspected $200$ manufactured widgets for defects. Carlos found $12$ defective widgets and Dana found $9$ defective widgets. Which explanation best accounts for the difference between their estimated defect rates?

The manufacturing process changed between Carlos's and Dana's inspections, so the rates must differ.

The difference is consistent with sampling variability because the observed difference is small relative to the standard errors and their $95 percent sign$ confidence intervals overlap.

The difference is significant because $0.015$ is greater than both individual standard errors, proving a real difference.

The estimates differ due to a calculation mistake since with $200$ observations such a difference cannot occur by chance.

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