Use the following information for questions:
A hypothesis test for a population proportion p is given below:
H 0 : p = 0.10
H a : p ≠ 0.10
For each sample size n and sample proportion $\hat{p}$ compute the value of the z-statistic.
-Sample size n = 500 and sample proportion $\hat{p}$ = 0.04. z-statistic = ?
A) -6.84
B) -4.47
C) 4.47
D) 6.84

Question

Use the following information for questions:
 A hypothesis test for a population proportion p is given below:
H 0 : p = 0.10
H a : p ≠ 0.10
For each sample size n and sample proportion $\hat{p}$ compute the value of the z-statistic.
-Sample size n = 500 and sample proportion $\hat{p}$ = 0.04. z-statistic = ?
A) -6.84
B) -4.47
C) 4.47
D) 6.84

Quizplus · Accepted Answer

The z-statistic is calculated using the formula $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$, where $\hat{p}$ is the sample proportion, $p_0$ is the hypothesized population proportion, and $n$ is the sample size. Plugging in the given values ($\hat{p} = 0.04$, $p_0 = 0.10$, $n = 500$), we get $z = \frac{0.04 - 0.10}{\sqrt{\frac{0.10(1-0.10)}{500}}} = -4.47$.

Use the Following Information for Questions: a Hypothesis Test p^\hat{p}p^​

Use the Following Information for Questions:
a Hypothesis Test $\hat{p}$