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 purchased this company's brand of the product.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

To find the observed z value, we need to calculate the sample proportion first:

p̂ = 50/144 = 0.3472

Then, we can calculate the standard error of the proportion:

SE(p̂) = sqrt(p̂(1-p̂)/n) = sqrt(0.3472(1-0.3472)/144) = 0.0485

Finally, we can calculate the observed z value:

z = (p̂ - p) / SE(p̂) = (0.3472 - 0.3) / 0.0485 = 1.2371

Rounding to two decimal places, we get z = 1.24, which is closest to choice D. Therefore, the answer is D.

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