Question 1
A $95\%$ confidence interval for $p_1-p_2$ is $(-0.08, 0.14)$. Which claim is best supported by this interval?
A. There is a clear difference between the two population proportions because $0$ is inside the interval. B. There is not enough evidence of a difference between the two population proportions because $0$ is inside the interval. C. Population 1 has a proportion exactly $0.08$ less than population 2. D. Population 1 has a proportion exactly $0.14$ greater than population 2.
Question 2
A $95\%$ confidence interval for $p_1-p_2$ is $(0.03, 0.19)$. Which conclusion is correct?
A. There is evidence that $p_1$ is greater than $p_2$ because the entire interval is above $0$. B. There is evidence that $p_1$ is less than $p_2$ because the entire interval is above $0$. C. There is not enough evidence of a difference because the interval contains positive values. D. The two population proportions must be equal because the interval does not include $0.03$.
Question 3
A student says, "The interval $(-0.12, 0.05)$ proves that $p_1$ is smaller than $p_2$." What is the best response?
A. The student is correct because the interval includes negative values. B. The student is incorrect because the interval includes $0$, so a difference of $0$ is still plausible. C. The student is correct because any interval with a negative value must mean $p_1<p_2$. D. The student is incorrect because confidence intervals can never be used to compare two proportions.
Question 4
Which confidence interval gives the strongest evidence that $p_1>p_2$?
A. $(-0.20, -0.02)$ B. $(-0.06, 0.04)$ C. $(0.01, 0.09)$ D. $(-0.03, 0.12)$
Question 5
A $90\%$ confidence interval for $p_1-p_2$ is $(-0.01, 0.17)$. Which statement is most accurate?
A. A difference of $0$ is plausible, so the interval does not give strong evidence of a difference. B. Population 1 is definitely greater than population 2. C. Population 2 is definitely greater than population 1. D. The exact difference between the proportions is $0.17$.
