Chi-Square Tests for Categorical Data · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Counts against the model

Mathematics · Data & Statistics · ages 21-22
Name ______________________   Date ____________

  1. In a contingency table a cell sits in a row totaling 30 and a column totaling 40, with 120 observations overall. Find its expected count.

    Answer: ______________

  2. A cell sits in a row totalling 30 and a column totalling 40, with 120 observations overall. Find its expected count.

    Answer: ______________

  3. A goodness of fit test uses 5 categories. How many degrees of freedom apply?

    • 5
    • 3
    • 4

  4. A contingency table has 3 rows and 4 columns. How many degrees of freedom does its test use?

    • 12
    • 6
    • 7

  5. One sample of students is sorted by grade level and by pet choice. Which test fits?

    • Homogeneity
    • Goodness of fit
    • Independence

  6. In one cell the observed count is 14 and the expected count is 10. Find that cell's contribution (O minus E) squared over E.

    Answer: ______________

  7. A goodness of fit test uses 5 categories. How many degrees of freedom apply?

    • 4
    • 5
    • 3
    • 6

  8. Under the claim of independence, what does a cell expect?

    • Row total times column total over grand total
    • Grand total divided by cell count
    • Its observed count

  9. Separate samples of voters are drawn in three cities and compared on one preferred policy. Which test fits?

    • Independence
    • Homogeneity
    • Goodness of fit with 3 categories

  10. A student rejects independence and claims one variable causes the other. What is the error?

    • Association alone never proves cause
    • The statistic should be zero
    • The degrees of freedom were wrong
LightMySky · lightmysky.comW1-mt_yxc87pzaXX-s1

Answer key

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

Counts against the model W1-mt_yxc87pzaXX-s1

  1. 10 · Row times column over total is 30 times 40 divided by 120, which is 10.
  2. 10 · Row times column over total is 30 times 40 divided by 120.
  3. 4 · One degree is lost because the counts must sum to the total, so 5 minus 1 is 4.
  4. 6 · Degrees of freedom are rows minus 1 times columns minus 1, which is 2 times 3.
  5. Independence · One sample sorted two ways asks whether the two variables are associated.
  6. 1.6 · The gap is 4, squared is 16, and 16 over 10 is 1.6.
  7. 4 · One degree is lost because the counts must sum to the total, so 5 minus 1 is 4.
  8. Row total times column total over grand total · Unrelated variables split proportionally, which gives that product rule.
  9. Homogeneity · Several samples compared on one trait is the homogeneity design.
  10. Association alone never proves cause · Rejecting the null shows an association, but cause needs a different design.
Worksheet · LightMySky