Hypothesis test for correlation Quiz

1. Which value cannot be a product moment correlation coefficient?

• A. $-0.9$
• B. $0$
• C. $1.2$
• D. $1$

2. Which are the correct hypotheses for a test for positive correlation?

• A. $H_0:r=0$, $H_1:r>0$
• B. $H_0:\rho=0$, $H_1:\rho>0$
• C. $H_0:\rho>0$, $H_1:\rho=0$
• D. $H_0:\rho=0$, $H_1:\rho\neq0$

3. A two-tailed test with $n=15$ has critical value $0.5140$ at 5%. Which $r$ leads to rejecting $H_0$?

• A. $0.45$
• B. $-0.52$
• C. $0.50$
• D. $-0.51$

4. A p-value of $0.07$ is found at the 5% level. What is the conclusion?

• A. Reject $H_0$
• B. Do not reject $H_0$
• C. $H_1$ is proved
• D. $H_0$ is proved true

5. A test finds significant positive correlation between ice cream sales and sunburn cases. Which is the best comment?

• A. Ice cream causes sunburn.
• B. Sunburn causes ice cream sales.
• C. A third factor such as hot weather may affect both.
• D. The test proves there is no link.