Hypothesis tests for correlation Quiz

1. Which hypothesis states that there is no linear correlation in the population?

• A. $H_0:r=0$
• B. $H_0:\rho=0$
• C. $H_0:\rho\ne0$
• D. $H_0:\rho=1$

2. $n=15$, $r=0.45$, $H_1:\rho>0$, one-tailed $5\%$ critical value $0.4409$. The conclusion is

• A. Reject $H_0$: evidence of positive correlation
• B. Do not reject $H_0$: no correlation
• C. Reject $H_0$: evidence of negative correlation
• D. The test cannot be done

3. For a two-tailed test at $5\%$ with critical values $\pm0.4438$, which value of $r$ leads to rejecting $H_0$?

• A. $0.40$
• B. $-0.40$
• C. $0.44$
• D. $-0.46$

4. A $p$-value of $0.03$ is given for a test at the $5\%$ significance level. The correct decision is

• A. Do not reject $H_0$
• B. Reject $H_0$
• C. Accept that $\rho=0$
• D. The significance level is invalid

5. A strong correlation between ice cream sales and sunburn cases is found. The best comment is

• A. Ice cream causes sunburn
• B. Sunburn causes ice cream sales
• C. Another factor, such as hot weather, may explain both
• D. The correlation must be zero