Hypothesis testing concepts Quiz

1. A die is suspected of landing on 6 more often than expected. Which hypotheses should be tested?

• A. $\mathrm{H}_0:p=\frac16,\ \mathrm{H}_1:p>\frac16$
• B. $\mathrm{H}_0:p=\frac16,\ \mathrm{H}_1:p\ne\frac16$
• C. $\mathrm{H}_0:p>\frac16,\ \mathrm{H}_1:p=\frac16$
• D. $\mathrm{H}_0:p=\frac16,\ \mathrm{H}_1:p<\frac16$

2. A two-tailed test is carried out at the $5\%$ significance level. What probability is allowed in each tail?

• A. $5\%$
• B. $10\%$
• C. $2.5\%$
• D. $0.25\%$

3. The test statistic lies in the critical region. Which conclusion is correct?

• A. $\mathrm{H}_1$ has been proved true
• B. Reject $\mathrm{H}_0$: there is sufficient evidence for $\mathrm{H}_1$
• C. Do not reject $\mathrm{H}_0$
• D. The sample is too small to decide

4. $X\sim\mathrm{B}(20,0.5)$ under $\mathrm{H}_0$, and $\mathrm{H}_1:p<0.5$ is tested at the $5\%$ level. Given $\mathrm{P}(X\le5)=0.0207$ and $\mathrm{P}(X\le6)=0.0577$, what is the critical region?

• A. $X\le6$
• B. $X\le4$
• C. $X\le9$
• D. $X\le5$

5. The critical region for a test on $\mathrm{B}(20,0.5)$ is $X\le5$ or $X\ge15$, and each tail has probability $0.0207$. What is the actual significance level?

• A. $0.0414$
• B. $0.05$
• C. $0.0207$
• D. $0.0577$