Past data indicates an 80% (0.8) success rate in treating a certain medical problem. A new treatment is used on 100 patients in a clinical trial. It is successful in 87% (0.87) of the cases. What is the value of the z-score that can be used to test the null hypothesis that the success rate is 80%?
A) 7
B) 2
C) 1.75
D) -1.75

Question

Quizplus · Accepted Answer

The z-score is calculated using the formula $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$, where $\hat{p}$ is the observed proportion (0.87), $p_0$ is the null hypothesis proportion (0.8), and $n$ is the sample size (100). Plugging in the values, we get $z = \frac{0.87 - 0.8}{\sqrt{\frac{0.8(0.2)}{100}}} = \frac{0.07}{\sqrt{0.0016}} = \frac{0.07}{0.04} = 1.75$.

Past Data Indicates an 80% (0