Language of hypothesis testing Quiz

1. A researcher wants to test whether the proportion $p$ of left-handed students is greater than 0.1. Which hypotheses?

• A. $H_0:p>0.1,\ H_1:p=0.1$
• B. $H_0:p=0.1,\ H_1:p\ne0.1$
• C. $H_0:p=0.1,\ H_1:p>0.1$
• D. $H_0:X=0.1,\ H_1:X>0.1$

2. Under $H_0$, $X\sim B(20,0.3)$ and the critical region is $X\ge10$. What is the actual significance level?

• A. $0.0480$
• B. $0.1133$
• C. $0.9520$
• D. $0.0171$

3. What is the $p$-value?

• A. The probability that $H_0$ is true
• B. The probability that $H_1$ is true
• C. The significance level of the test
• D. The probability of a result at least as extreme as observed, if $H_0$ is true

4. In a two-tailed test at the 10% significance level, what probability is allowed in each tail?

• A. $10\%$
• B. $5\%$
• C. $20\%$
• D. $2.5\%$

5. The observed value lies in the acceptance region. What is the correct conclusion?

• A. $H_0$ is proved true
• B. $H_1$ is true
• C. There is insufficient evidence to reject $H_0$
• D. Reject $H_0$