Hypothesis tests for a binomial proportion Quiz

1. $X\sim B(15,0.85)$ under $H_0$, $H_1:p<0.85$, and 10 successes are observed. The $p$-value is...

• A. $P(X\ge10)$
• B. $P(X\le10)$
• C. $P(X<10)$
• D. $P(X=10)$

2. In a two-tailed test at the 5% level, an upper-tail $p$-value is compared with...

• A. $0.05$
• B. $0.10$
• C. $0.95$
• D. $0.025$

3. A test at the 5% level rejects $H_0$. Which statement is correct?

• A. There is evidence at the 5% level that $p$ differs from the claimed value in the direction of $H_1$
• B. $H_1$ has been proved true
• C. The probability that $H_0$ is true is less than 5%
• D. The sample proportion equals the population proportion

4. A significance level of 5% means...

• A. the sample is 5% of the population
• B. $H_1$ is true with probability 5%
• C. there is a 5% chance of rejecting $H_0$ when it is true
• D. the test is 5% accurate

5. $X\sim B(20,0.3)$, $H_1:p>0.3$, 5% level. Given $P(X\ge9)=0.1133$ and $P(X\ge10)=0.0480$, the critical region is...

• A. $X\ge9$
• B. $X\ge10$
• C. $X\ge11$
• D. $X\le10$