A company believes that it controls more than 30% of the total market share for one of its products.To prove this belief, a random sample of 144 purchases of this product is contacted.It is found that 50 of the 144 purchases were of this company's brand.If a researcher wants to conduct a statistical test for this problem, the observed z value would be _______.
A)0.05
B)0.103
C)0.35
D)1.24
E)1.67

Question

Quizplus · Accepted Answer

The observed z value is calculated using the formula for a proportion z-test: $z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$, where $\hat{p}$ is the sample proportion, $p_0$ is the null hypothesis proportion (in this case, 0.30), and $n$ is the sample size. Here, $\hat{p} = \frac{50}{144}$, so the calculation is $z = \frac{\frac{50}{144} - 0.30}{\sqrt{\frac{0.30(1-0.30)}{144}}}$, which results in a z value of approximately 1.24.

A Company Believes That It Controls More Than 30% of the Total