Suppose that the following is to be tested: $\mathrm { H } _ { 0 } : \mathrm { p } = 0.72$ and $\mathrm { H } _ { \mathrm { a } } : \mathrm { p } \neq 0.72$. Calculate the observed z-statistic for the following sample data: Sixty-eight out of ninety test subjects have the characteristic of interest. Round to the nearest thousandth.
A) $z = 0.751$
B) $z = 0.756$
C) $z = - 0.751$
D) $\mathrm { z } = 0.453$

Question

Quizplus · Accepted Answer

The observed z-statistic is calculated as:$$z = \frac{\hat{p} - p_0}{\sqrt{p_0(1-p_0)/n}}$$where $\hat{p}$ is the sample proportion, $p_0$ is the hypothesized proportion, and $n$ is the sample size.In this case, $\hat{p} = 68/90 = 0.756$, $p_0 = 0.72$, and $n = 90$. Plugging these values into the formula, we get:$$z = \frac{0.756 - 0.72}{\sqrt{0.72(1-0.72)/90}} = 0.751$$Therefore, the observed z-statistic is 0.751, which is closest to choice A.

Suppose That the Following Is to Be Tested H0:p=0.72\mathrm { H } _ { 0 } : \mathrm { p } = 0.72H0​:p=0.72

Suppose That the Following Is to Be Tested $\mathrm { H } _ { 0 } : \mathrm { p } = 0.72$