4.18 Hypothesis testing: means, proportions, correlation and errors Quiz

1. A test rejects $\mathrm{H}_0$ although $\mathrm{H}_0$ is true. What type of error is this?

• A. Type I
• B. Type II
• C. Type III
• D. No error

2. A correlation test of $\mathrm{H}_0:\rho=0$ gives $p=0.031$. What is the conclusion at the $5\%$ level?

• A. Accept that $\rho=0$.
• B. Reject $\mathrm{H}_0$: sufficient evidence of linear correlation.
• C. Prove that one variable causes the other.
• D. The test is invalid.

3. A sample of $9$ has unknown $\sigma$. Which test is used for the mean?

• A. $z$-test
• B. Binomial test
• C. One-sample $t$-test
• D. Poisson test

4. $X\sim\mathrm{B}(15,\ 0.4)$ under $\mathrm{H}_0$, with $\mathrm{H}_1:p>0.4$ at the $5\%$ level. $\mathrm{P}(X\ge9)=0.0950$ and $\mathrm{P}(X\ge10)=0.0338$. What is the critical region?

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

5. For a test with a critical region $X\le10$, the probability of a Type II error is found by calculating...

• A. $\mathrm{P}(X\le10)$ under $\mathrm{H}_0$
• B. $\mathrm{P}(X\ge11)$ under the true parameter value
• C. $\mathrm{P}(X\le10)$ under the true parameter value
• D. $1-\mathrm{P}(X\ge11)$ under $\mathrm{H}_0$