Chi-squared goodness of fit tests Quiz

1. A fair die is thrown 90 times. What is the expected frequency of each face?

• A. $15$
• B. $6$
• C. $30$
• D. $90$

2. Observed frequencies in 4 cells are tested against a Poisson model whose mean was estimated from the data. How many degrees of freedom are there (no cells combined)?

• A. $3$
• B. $2$
• C. $1$
• D. $4$

3. Which set of expected frequencies shows that cells must be combined?

• A. $12,\ 8,\ 4.5,\ 3$
• B. $12,\ 8,\ 6,\ 5$
• C. $10,\ 10,\ 10,\ 10$
• D. $20,\ 15,\ 5,\ 5$

4. Waiting times are modelled as uniform on 0 to 20 minutes, with 200 observations. What is the expected frequency for the class 5 to 10 minutes?

• A. $25$
• B. $50$
• C. $40$
• D. $100$

5. The test statistic is $X^2=7.1$ and the 5% critical value of $\chi^2_3$ is $7.815$. What is the conclusion?

• A. Reject $H_0$; the model does not fit
• B. The test must be repeated with $\nu=4$
• C. Insufficient evidence to reject $H_0$; the model is suitable
• D. Accept $H_1$ with 95% certainty