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Grade 11 · Math · Algebra 2

11th grade Confidence intervals from a sample, for averages and for percents worksheet

6 printable versionsChallenge Me10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Confidence intervals from a sample, for averages and for percents

Grade 11 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

  1. In Ari's random sample of 400 students, a proportion 0.4 want a later start. Using 1.96, what is the upper end of the 95% interval, as a percent?

  2. In Bo's random sample of 100 shoppers, a proportion 0.5 bring their own bags. Using 1.96, what is the upper end of the 95% interval, as a percent?

  3. In Esme's random sample of 100 bikes at school, a proportion 0.2 have bells (ring ring). Using 1.96, what is the upper end of the 95% interval, as a percent?

  4. For the same n, which sample proportion gives Kira the widest interval?

    • p = 0.1
    • p = 0.5
    • p = 0.9

  5. Milo's 95% interval for mean sleep is 7.6 to 8.2 hours. Milo says 95% of students sleep 7.6 to 8.2 hours. Agree or disagree?

    • Agree: 95% of the data lie inside
    • Disagree: it's about the mean
    • Agree: 7.6 is the smallest

  6. Noah's 95% interval for mean homework time is 40 to 50 minutes. Noah says nearly every student does 40 to 50 minutes. Agree or disagree?

    • Agree: the interval holds the data
    • Agree: 95% means nearly the whole class
    • Disagree: single students vary more

  7. Pia says a bigger sample always makes the interval wider. Agree or disagree?

    • Agree: n is in the margin
    • Disagree: it gets narrower
    • Agree: more data, more spread

  8. Ren's 95% interval is 35.2% to 44.8%. Someone claims half of all students want a later start. Is that believable?

    • No: 50% is outside the interval
    • Yes: 50% is close enough to count
    • Yes: 40% rounds to 50%

  9. Tala's 95% interval for mean ride time is 33.04 to 36.96 minutes. Is a true mean of 35 minutes believable?

    • Yes: it's inside the interval
    • No: 33.04 is the one possible value
    • No: it must equal an end

  10. Class A's interval is 60% to 70% and class B's is 75% to 85%. What does Zee conclude?

    • A's true percent is likely higher
    • B's true percent is likely higher
    • They are surely the same
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11th grade Confidence intervals from a sample, for averages and for percents worksheet – printable
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About this worksheet

Confidence intervals from a sample, for averages and for percents. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find the standard error of a mean, s ÷ √n, and of a proportion, √(p(1 − p) ÷ n).
  • I can read the multiplier from a table (1.645, 1.96, 2.576) and build an interval from sample data.
  • I can say how sample size and confidence level change the width.
  • I can say what an interval does and doesn't claim, and use it to judge a claim.

Standard: S-IC.B.4

Words to know

confidence interval: A range of believable values for the true mean or percent

standard error: How much a sample result tends to vary

margin of error: Multiplier × standard error, added and subtracted

multiplier z*: A table number for the confidence level

sample proportion p: The share of the sample with the trait

Common mistakes

Your child divided by n. The standard error of a mean divides the SD by the square root of n.

Your child found the standard error but didn't multiply by the table's 1.96. The margin of error is multiplier × standard error.

Your child used the rough margin 1 ÷ √n. With the sample's own percent, the margin is 1.96 × √(p(1 − p) ÷ n).

Questions parents ask

What is the most common mistake with confidence intervals from a sample, for averages and for percents?

Your child divided by n. The standard error of a mean divides the SD by the square root of n.

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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