Question

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 _______.

Answer 1

Answer: 1.24

Step-by-step explanation:

Let p be the population proportion of the total market share for one of its products.

As per given , we have

p=0.30

Sample size : n= 144

Sample proportion : $\hat{p}=\dfrac{50}{144}=0.347222222222\approx0.3472$

Formula for z-value :-

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

i.e. $z=\dfrac{0.3472-0.30}{\sqrt{\dfrac{0.30(1-0.30)}{144}}}$

Simplify ,

. $z=1.2359861303\approx1.24$

Hence, the observed z value would be 1.24 .