Choosing and critiquing statistical models Quiz

1. Which of these is NOT a condition for $X\sim B(n,p)$?

• A. Fixed number of trials
• B. Independent trials
• C. The variable is continuous
• D. Constant probability of success

2. Four sweets are taken without replacement from a bag of $10$ sweets, of which $3$ are red, and the number of red sweets is counted. Why is a binomial model not exact?

• A. The number of trials is not fixed
• B. The trials are not independent
• C. There are more than two outcomes
• D. The probability of red is $0.3$

3. A continuous data set has mean $12$ and median $7$. Which statement is most reasonable?

• A. The data are symmetrical, so a Normal model is suitable
• B. The data are negatively skewed, so a Normal model is suitable
• C. The data are positively skewed, so a Normal model is doubtful
• D. The data must be discrete

4. A Normal model predicts $5$ values above a threshold in a sample, and $22$ are observed. The best comment is

• A. The model is a good fit
• B. The model underestimates the upper tail
• C. The model overestimates the upper tail
• D. The sample is too small to compare

5. For $X\sim B(40,0.3)$, the mean is

• A. $12$
• B. $8.4$
• C. $28$
• D. $0.3$