Part 7 of 8

The 95% confidence interval of for the annual return is (
[ Select ]
-0.0536
-0.028
-0.0012
,
[ Select ]
0.0792
0.0536
0.0524
)

Question

Part 7 of 8

The 95% confidence interval of for the annual return is ( 
[ Select ]
-0.0536
-0.028
-0.0012
   , 
[ Select ]
0.0792
0.0536
0.0524
 )

BlackTom AI · Accepted Answer

The problem presents a fill-in-the-blank style question for a 95% confidence interval of an annual return, with two dropdowns to choose the lower and upper endpoints. The selections provided as the correct answer are -0.028 for the lower bound and 0.0792 for the upper bound. Below, I evaluate the available options for each dropdown and explain why the selected pair makes sense, while pointing out why the other choices are not selected.

Lower bound options (for the first dropdown): -0.0536, -0.028, -0.0012

- Option lower bound -0.0536: If this were chosen as the lower bound, the corresponding upper bound could be any of the positive options (0.0792, 0.0536, or 0.0524). While -0.0536 is a valid lower bound in isolation (it is less than zero), selecting it would typically yield a wider interval than the one implied by the provided correct answer. Since the given answer uses -0.028 as the lower bound, -0.0536 is not the chosen lower limit in this question.
- Option lower bound -0.028: This value is negative and closer to zero than -0.0536, producing a narrower interval width than using -0.0536 while still potentially spanning zero if the upper bound is positive. The provided correct answer selects -0.028, which aligns with a plausible 95% CI that includes some positive return but not a very large negative tail.
- Option lower bound -0.0012: This is a very small negative (almost zero) lower bound. If paired with a positive upper bound, the interval would be quite narrow and would reflect a substantial degree of uncertainty with a point estimate near zero. This pairing is not chosen in the supplied answer, so it is considered incorrect within the given key.

Upper bound options (for the second dropdown): 0.0792, 0.0536, 0.0524

- Option upper bound 0.0792: This is a relatively large positive upper bound among the options and, when paired with a lower bound near -0.028, yields a wide interval that crosses zero. This pairing matches the provided correct answer of (-0.028, 0.0792), suggesting a conclusion that the annual return is not statistically different from zero at the 5% level.
- Option upper bound 0.0536: This upper bound is smaller than 0.0792. If paired with the negative lower bound -0.028, the interval would be (-0.028, 0.0536), which still crosses zero but would be narrower. Since the key indicates the upper bound should be 0.0792, 0.0536 is not selected in the correct answer here.
- Option upper bound 0.0524: This is another relatively small positive upper bound. Paired with -0.028, it would give (-0.028, 0.0524), a narrower interval than the one indicated by the provided correct answer. It is not the selected upper bound in the given key.

Putting it together, the only pairing that matches the supplied answer is a lower bound of -0.028 with an upper bound of 0.0792. This combination yields a 95% CI that includes zero and reflects a modestly positive central tendency with appreciable uncertainty, which is a common scenario for annual return estimates.

In summary, evaluating all combinations of the available lower and upper options shows that:
- The lower bound -0.028 is the chosen option because it, when paired with the upper bound 0.0792, produces the interval (-0.028, 0.0792) that aligns with the provided correct answer.
- The other lower bound choices (-0.0536, -0.0012) either produce wider or narrower intervals than the one implied by the key, and are therefore not selected in the given solution.
- The other upper bound choices (0.0536, 0.0524) would yield narrower intervals when paired with -0.028, which do not match the provided correct pair, hence are not chosen in the key.

Thus, the reasoning supports selecting -0.028 as the lower bound and 0.0792 as the upper bound for the 95% confidence interval.

COMM_V 298 101 102 103 2025W1 Class 12 and 13 Practice Quiz

Part 7 of 8 The 95% confidence interval of for the annual return is ( [ Select ] -0.0536 -0.028 -0.0012 , [ Select ] 0.0792 0.0536 0.0524 )

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Part 7 of 8 The 95% confidence interval of for the annual return is ( [ Select ] -0.0536 -0.0012 -0.028 , [ Select ] 0.0792 0.0524 0.0536 )

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