Hypothesis tests for binomial and Poisson Quiz

1. $X\sim\mathrm{B}(15,0.5)$ under $\mathrm{H}_0$ and $\mathrm{H}_1:p>0.5$ is tested at the $5\%$ level. Given $\mathrm{P}(X\ge11)=0.0592$ and $\mathrm{P}(X\ge12)=0.0176$, what is the critical region?

• A. $X\ge11$
• B. $X\ge12$
• C. $X\ge13$
• D. $X\ge10$

2. Calls arrive at a mean rate of $3$ per hour. To test whether the rate has changed, calls are counted over $5$ hours. What is the distribution of $X$ under $\mathrm{H}_0$?

• A. $\mathrm{Po}(3)$
• B. $\mathrm{Po}(5)$
• C. $\mathrm{Po}(15)$
• D. $\mathrm{Po}(0.6)$

3. For $X\sim\mathrm{B}(20,0.7)$, how can $\mathrm{P}(X\le10)$ be found from tables for $Y\sim\mathrm{B}(20,0.3)$?

• A. $\mathrm{P}(Y\le10)$
• B. $\mathrm{P}(Y\le9)$
• C. $\mathrm{P}(Y\ge11)$
• D. $\mathrm{P}(Y\ge10)$

4. $X\sim\mathrm{B}(100,0.4)$ is approximated by a normal distribution. Find $\mathrm{P}(X\ge48)$.

• A. $0.0629$
• B. $0.0512$
• C. $0.0414$
• D. $0.0765$

5. A two-tailed test at the $5\%$ level gives an upper-tail probability of $0.03$ for the observed value. What is the conclusion?

• A. Reject $\mathrm{H}_0$, because $0.03<0.05$
• B. Do not reject $\mathrm{H}_0$, because $0.03>0.025$
• C. Reject $\mathrm{H}_0$, because $0.03>0.025$
• D. Do not reject $\mathrm{H}_0$, because $0.03<0.05$