Confidence Intervals for Means and Proportions · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Intervals that trap the truth

Mathematics · Data & Statistics · ages 20-21
Name ______________________   Date ____________

  1. A 95 percent interval for a mean is (46, 54). What is the sample mean?

    • 50
    • 48
    • 52
    • 46

  2. A sample of 25 has standard deviation 10. Using 2 as the approximate 95 percent multiplier, find the margin of error.

    Answer: ______________

  3. A sample of 25 has standard deviation 10. Using 2 as the 95 percent multiplier, find the margin of error.

    Answer: ______________

  4. A mean interval uses 16 observations with unknown sigma. Which distribution fits?

    • The z distribution
    • The t distribution with 16 degrees of freedom
    • The t distribution with 15 degrees of freedom

  5. Theo says there is a 95 percent chance the true mean lies inside the computed interval (46, 54). Is Theo right?

    Circle one:   True   False

  6. A mean interval uses 16 observations with unknown sigma. Which distribution fits?

    • The t distribution with 15 degrees of freedom
    • The z distribution
    • The t distribution with 16 degrees of freedom
    • The chi-square distribution

  7. Theo says there is a 95 percent chance the true mean lies inside the computed interval (46, 54). Is Theo right?

    Circle one:   True   False

  8. In 200 trials there are 60 successes. Give the sample proportion as a decimal.

    Answer: ______________

  9. Ann says about 95 percent of intervals from repeats would trap the mean. Ben says this one interval has a 95 percent chance of trapping it. Who is right?

    • Ben
    • Ann
    • Both

  10. A sample of 25 has standard deviation 15. Using 2 as the 95 percent multiplier, find the margin of error.

    Answer: ______________

LightMySky · lightmysky.comW1-mt_Pg2fPDW1sn-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

Intervals that trap the truth W1-mt_Pg2fPDW1sn-s1

  1. 50 · The interval centres on the sample mean, and the midpoint of 46 and 54 is 50.
  2. 4 · Standard error is 10 over 5, which is 2, and twice that is 4.
  3. 4 · Standard error is 10 over 5, which is 2, and twice that is 4.
  4. The t distribution with 15 degrees of freedom · Estimated sigma means t, with degrees of freedom one fewer than the sample size.
  5. False · The 95 percent describes repeats of the method, not the chance for one finished interval.
  6. The t distribution with 15 degrees of freedom · Sigma is estimated from a small sample, so use t with n minus 1, which is 15, degrees of freedom.
  7. False · Theo is wrong. The 95 percent describes the method over many repeats, not the chance for one finished interval.
  8. 0.3 · The sample share is 60 over 200.
  9. Ann · The level belongs to the long run procedure, so Ann reads it correctly.
  10. 6 · Standard error is 15 over 5, which is 3, and twice that is 6.
Worksheet · LightMySky