Language of hypothesis testing Quiz

1. A manufacturer claims that $p=0.2$. A customer thinks $p$ is higher. Which are the hypotheses?

• A. $H_0:p=0.2,\ H_1:p<0.2$
• B. $H_0:p=0.2,\ H_1:p>0.2$
• C. $H_0:p>0.2,\ H_1:p=0.2$
• D. $H_0:p=0.2,\ H_1:p\ne0.2$

2. For $X\sim B(20,0.5)$ and $H_1:p<0.5$ at 5%, $P(X\le5)=0.0207$ and $P(X\le6)=0.0577$. What is the critical region?

• A. $X\le6$
• B. $X\le5$
• C. $X\le4$
• D. $X\ge15$

3. What does a significance level of 5% mean?

• A. The probability that $H_0$ is true is 5%
• B. The probability that $H_1$ is true is 5%
• C. The probability of rejecting $H_0$ when it is true is 5%
• D. The sample is 5% of the population

4. A 1-tail test at 5% gives a $p$-value of $0.032$. What is the conclusion?

• A. Reject $H_0$
• B. Do not reject $H_0$
• C. $H_0$ is proved true
• D. The test is invalid

5. In a 2-tail test at 10%, the lower tail has probability $0.04$ for the observed value. Which statement is correct?

• A. The lower tail is too large because $0.04>0.01$, so $H_0$ is not rejected
• B. The lower tail is within the $0.05$ allowed, so the value is in the critical region
• C. The result is not significant because $0.04<0.10$
• D. The probability must be doubled to $0.08$ and compared with $0.05$