Hypothesis test for the parameter of a geometric distribution Quiz

1. $\mathrm{H}_0:p=0.25$, $\mathrm{H}_1:p>0.25$ and the first success is on trial $2$. Which probability do you find?

• A. $\mathrm{P}(X\geq2)$
• B. $\mathrm{P}(X=2)$
• C. $\mathrm{P}(X\leq2)$
• D. $\mathrm{P}(X>2)$

2. $\mathrm{H}_0:p=0.1$, $\mathrm{H}_1:p<0.1$ and the first success is on trial $20$. Find the probability to compare.

• A. $0.9^{20}$
• B. $0.9^{19}$
• C. $1-0.9^{19}$
• D. $0.1\times0.9^{19}$

3. Which is the correct pair of hypotheses for 'the probability of success is not $0.4$'?

• A. $\mathrm{H}_0:p=0.4,\ \mathrm{H}_1:p<0.4$
• B. $\mathrm{H}_0:p\neq0.4,\ \mathrm{H}_1:p=0.4$
• C. $\mathrm{H}_0:p=0.4,\ \mathrm{H}_1:p>0.4$
• D. $\mathrm{H}_0:p=0.4,\ \mathrm{H}_1:p\neq0.4$

4. $\mathrm{H}_0:p=0.5$, $\mathrm{H}_1:p<0.5$ at $5\%$. What is the critical region?

• A. $X\geq6$
• B. $X\geq4$
• C. $X\geq5$
• D. $X\leq5$

5. For which situation is the geometric model for a test most doubtful?

• A. Rolling a fair die until a six appears
• B. Testing items from a large batch with a constant defect rate
• C. A player's attempts at a game level, where they improve with each attempt
• D. Tossing a coin until the first head