Part 3 of 3

The 95% Confidence Interval is ( -0.2158 , 0.2186 )

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Part 3 of 3

The 95% Confidence Interval is ( -0.2158 , 0.2186 )

BlackTom AI · Accepted Answer

Let's start by identifying what the given data represents. The statement provides a 95% confidence interval: (-0.2158, 0.2186). In a typical interval estimate, these two numbers are the lower and upper bounds for the parameter of interest, such as a population mean difference or a regression coefficient.

Option content recall: for a multiple_dropdowns_question, you would usually select the appropriate values to fill in the lower and upper bounds. Here, the two values to select are -0.2158 and 0.2186, corresponding respectively to the left (lower) bound and the right (upper) bound of the interval.

Interpretation of the interval: this CI means we are 95% confident that the true parameter lies somewhere between -0.2158 and 0.2186. A key consequence is that zero is contained within this interval, which has implications for statistical significance if the parameter being estimated tests against zero.

What each bound implies:
- The lower bound (-0.2158) indicates the smallest value the parameter could plausibly take with 95% confidence, given the data and model.
- The upper bound (0.2186) indicates the largest plausible value under the same confidence level.

Common misconception check: some might think the CI asserts the exact probability of the parameter being within the interval. In frequentist terms, the interpretation is about long-run frequency of intervals from repeated samples, not about the probability of the parameter itself lying in a single interval. Also, because zero is within (-0.2158, 0.2186), the interval does not provide evidence against a null hypothesis that the parameter equals zero at the 5% significance level, assuming a two-sided test was intended.

If you were asked to select the two values for the dropdowns, you would pair the smaller number with the left-hand slot and the larger number with the right-hand slot, yielding the bounds as listed. Any other pairing would invert the interval and misrepresent the estimate.

Note on completeness: the question text does not include any alternative options to compare against, so this reasoning focuses on the correct interpretation and placement of the two provided bounds within a 95% confidence interval framework.

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

Part 3 of 3 The 95% Confidence Interval is ( -0.2158 , 0.2186 )

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