Goodness of fit tests and contingency tables Quiz

1. A die is rolled 90 times to test whether it is fair. What is the expected frequency of each face?

• A. $6$
• B. $15$
• C. $18$
• D. $90$

2. A contingency table has 2 rows and 4 columns, with no cells combined. How many degrees of freedom does the test have?

• A. $8$
• B. $7$
• C. $4$
• D. $3$

3. A $\mathrm{B}(5,p)$ model, with $p$ estimated from the data, is fitted. After combining cells there are 5 cells. Find $\nu$.

• A. $3$
• B. $4$
• C. $2$
• D. $5$

4. In a goodness of fit test, one cell has $O=18$ and $E=12$. What does that cell contribute to $X^2$?

• A. $1.5$
• B. $0.5$
• C. $3$
• D. $6$

5. Expected frequencies are $20.4, 12.1, 6.3, 4.2, 3.0$. What should be done before calculating $X^2$?

• A. Nothing; the test can go ahead
• B. Delete the last two cells
• C. Combine the last two cells into one with $E=7.2$
• D. Combine the last two cells but keep $\nu$ the same