Hypothesis test for a binomial proportion Quiz

1. A test has $H_0:p=0.4$ and $H_1:p<0.4$ with $X\sim B(10,0.4)$. The observed value is 1. Which is the $p$-value?

• A. $P(X=1)$
• B. $P(X\le1)$
• C. $P(X\ge1)$
• D. $P(X\le0)$

2. $H_1:p>0.2$ with $X\sim B(15,0.2)$ and observed value 6. Which expression gives the $p$-value?

• A. $P(X\le5)$
• B. $1-P(X\le6)$
• C. $P(X=6)$
• D. $1-P(X\le5)$

3. A two-tailed test at 5% has an upper-tail probability $P(X\ge x)=0.03$. What is the decision?

• A. Reject $H_0$, as $0.03<0.05$
• B. Do not reject $H_0$, as $0.03>0.025$
• C. Reject $H_0$, as $0.03>0.025$
• D. Do not reject $H_0$, as $0.03<0.05$

4. Which is the best wording when $H_0$ is not rejected in a test of whether pass rates have increased?

• A. The pass rate has not increased
• B. The pass rate is proved to be unchanged
• C. There is insufficient evidence that the pass rate has increased
• D. The test is wrong

5. A test is carried out at the 1% significance level. What is 1%?

• A. The probability that $H_0$ is true
• B. The probability of incorrectly rejecting $H_0$
• C. The probability that $H_1$ is true
• D. The percentage of the population sampled