Sums of Poisson variables and Poisson hypothesis tests Quiz

1. $X\sim\mathrm{Po}(2)$ and $Y\sim\mathrm{Po}(5)$ are independent. What is the distribution of $X+Y$?

• A. $\mathrm{Po}(10)$
• B. $\mathrm{Po}(3.5)$
• C. $\mathrm{Po}(7)$
• D. $\mathrm{Po}(3)$

2. $X\sim\mathrm{Po}(1.5)$ and $Y\sim\mathrm{Po}(1.5)$ are independent. Find $\mathrm{P}(X+Y=3)$.

• A. $0.2240$
• B. $0.1255$
• C. $0.4232$
• D. $0.0498$

3. A manager claims the mean number of faults per day has increased from 6. Which are the correct hypotheses?

• A. $\mathrm{H}_0:\lambda=6,\ \mathrm{H}_1:\lambda<6$
• B. $\mathrm{H}_0:\lambda>6,\ \mathrm{H}_1:\lambda=6$
• C. $\mathrm{H}_0:\lambda=6,\ \mathrm{H}_1:\lambda\ne6$
• D. $\mathrm{H}_0:\lambda=6,\ \mathrm{H}_1:\lambda>6$

4. $\mathrm{H}_0:\lambda=3$, $\mathrm{H}_1:\lambda>3$. One observation of 7 gives $\mathrm{P}(X\ge7)=0.0335$. What is the conclusion at the 5% level?

• A. Do not reject $\mathrm{H}_0$ because $0.0335<0.05$
• B. Reject $\mathrm{H}_0$ because $0.0335<0.05$
• C. Reject $\mathrm{H}_0$ because $0.0335>0.025$
• D. Do not reject $\mathrm{H}_0$ because $0.0335>0.025$

5. A two-tailed test at the 10% level gives a lower-tail probability of $0.07$. What is the conclusion?

• A. Reject $\mathrm{H}_0$ because $0.07<0.10$
• B. Reject $\mathrm{H}_0$ because $0.07>0.05$
• C. Do not reject $\mathrm{H}_0$ because $0.07>0.05$
• D. Do not reject $\mathrm{H}_0$ because $0.07<0.10$