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
)

Question

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
 )

BlackTom AI · Accepted Answer

The question asks us to select the two bounds for a 95% confidence interval of the annual return using two dropdowns. The provided correct answer indicates the left bound should be -0.028 and the right bound should be 0.0792, forming the interval (-0.028, 0.0792).

Analyzing the left-bound options:
- Option -0.0536: Choosing -0.0536 as the left end would produce a much wider interval with the same or a similar right end; while wider intervals are possible, this would imply a different interval than the given correct pairing (-0.028, 0.0792). If the left bound were -0.0536, the set of potential right bounds among the provided options would need to correspond to a consistent, plausible CI; the given correct answer does not pair -0.0536 with 0.0792, so this option is inconsistent with the stated correct pairing.
- Option -0.0012: Selecting -0.0012 as the left bound would place the interval very close to zero on the negative side. Depending on the point estimate and standard error, this could be plausible, but it would not align with the demonstrated correct pair (-0.028, 0.0792). It also suggests a CI that is centered much closer to zero, which would typically occur with a smaller standard error or a different estimate, making it inconsistent with the provided correct interval.
- Option -0.028: This left bound is the correct left edge in the given solution. It sits below the (implied) point estimate and, when paired with the specified right bound, yields a balanced interval that spans negative to positive territory, which is a common form for annual return CIs.

Analyzing the right-bound options:
- Option 0.0792: This is the right edge in the provided correct pairing. It yields a wide interval that crosses into positive territory, which can occur with notable variability in annual returns; it also ensures the left bound -0.028 remains well below the right bound, preserving a valid interval.
- Option 0.0524: If this were the right bound, the interval would be narrower than the one indicated by the correct pair when paired with a left bound like -0.028. Since the target answer uses 0.0792 as the upper limit, choosing 0.0524 would not reproduce the same interval, and would imply a different estimate precision.
- Option 0.0536: Similar to 0.0524, this upper bound would produce a relatively narrow interval compared to 0.0792. Using this value would again define a different CI than the one indicated by the correct answer.

Putting it together, the pair (-0.028, 0.0792) forms a coherent 95% CI with a negative lower bound and a substantial positive upper bound, which aligns with the notion of notable variability in annual returns and a CI that straddles zero. The other left options (-0.0536, -0.0012) and the other right options (0.0524, 0.0536) would yield different intervals and do not match the stated correct pairing.

In summary, selecting -0.028 as the left bound and 0.0792 as the right bound is consistent with the provided correct answer and with the general interpretation of a 95% confidence interval for an annual return that spans negative to positive territory, reflecting uncertainty in the estimate.

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 -0.0012 -0.028 , [ Select ] 0.0792 0.0524 0.0536 )

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