What is the margin of error? Remember to use the same standard error you calculated in Question 7.24.

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To analyze the options for the margin of error, we first recall that the margin of error (MOE) is computed using the standard error from Question 7.24 multiplied by the appropriate critical value (from the z or t distribution) for the desired confidence level.
Option 1: 9.03. This value aligns with a typical MOE calculation when the SE from Q7.24 is multiplied by the corresponding critical value (for example, a z*SE or t*SE). If the SE you calculated in Question 7.24 and the chosen critical value yield 9.03, this option would be consistent with that process.
Option 2: 8.72. This is close to 9.03 but not identical. If the critical value or SE were slightly different, or if rounding occurred at an intermediate step, one might see a nearby figure like 8.72. However, without a matching product of the exact SE and the exact critical value from the problem, this would generally indicate a mismatch with the specified calculation.
Option 3: 4.36. This value is roughly half of 8.72 or 9.03, suggesting it could arise if a much smaller critical value was used or if the SE were misapplied (for instance, using half of the MOE inadvertently or applying a different portion of the formula). In standard MOE computations, such a small figure typically signals a miscalculation rather than a direct consequence of the intended formula.
Option 4: 18.06. This is roughly double 9.03, which would occur if the critical value or the standard error were mistakenly inflated (for example, multiplying by a critical value that's twice as large, or double-counting the SE). In well-formed margin-of-error calculations for the same confidence level and dataset, such a doubling would indicate an error in applying the formula or in the inputs rather than a correct result.
Across these options, the key distinction lies in whether the value reflects the exact product of the previously determined SE and the specific critical value required by the problem, including any rounding rules. The option that consistently matches the prescribed calculation steps from Question 7.24 should be the one that corresponds to the margin of error intended by the exercise, while the others reveal plausible misapplications or rounding variations.

FA25_QTM_100_3 7.26: Diamonds, Part II. - Requires Respondus LockDown Browser

What is the margin of error? Remember to use the same standard error you calculated in Question 7.24.

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