Confidence Intervals

Learn confidence-interval construction, margin and total width.

Lesson 1 of 32 parts Practice Flashcards

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Confidence-Interval Construction

Objective: Explain confidence-interval construction, apply the stated method, and check its conditions.

A common interval form is estimate ± critical multiplier·SE under the procedure’s assumptions. The multiplier depends on confidence level and reference distribution, such as normal or t. A supplied multiplier of 2 is a classroom input, not a universally exact 95% multiplier. Check the procedure and multiplier before interpreting coverage.

Formulas

$Interval = estimate ± c*SE$

Worked examples

Try itA synthetic estimate is 7 with SE=6 and critical multiplier 2. Find the lower endpoint of estimate ±2SE.Show answer

Step 1: Compute margin of error: 2SE. Step 2: The margin is 12. Step 3: Lower endpoint=7−12=-5; the multiplier is supplied, not universally exact for 95%.

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Confidence-Interval Construction

Objective: Explain confidence-interval construction, apply the stated method, and check its conditions.

Formulas

$Interval = estimate ± c*SE$

Worked examples

Try itA synthetic estimate is 7 with SE=6 and critical multiplier 2. Find the lower endpoint of estimate ±2SE.Show answer

Step 1: Compute margin of error: 2SE. Step 2: The margin is 12. Step 3: Lower endpoint=7−12=-5; the multiplier is supplied, not universally exact for 95%.

Margin and Total Width

Objective: Explain margin and total width, apply the stated method, and check its conditions.

Margin of error is the one-sided distance from the estimate to an endpoint in a symmetric interval. Total width is twice that margin. Changing confidence level, variability, or sample size changes width under a specified interval procedure. Do not confuse a one-sided margin with full interval width.

Formulas

$Width=2·margin=2c*SE$

Worked examples

Try itA synthetic interval uses estimate 7 ± 2(6). Find the total interval width.Show answer

Step 1: The margin is 2a on each side. Step 2: Width is twice the margin: 2·12. Step 3: The width is 24.

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