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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 _______.

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JeanaShupp

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 : [tex]\hat{p}=\dfrac{50}{144}=0.347222222222\approx0.3472[/tex]

Formula for z-value :-

[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]

i.e. [tex]z=\dfrac{0.3472-0.30}{\sqrt{\dfrac{0.30(1-0.30)}{144}}}[/tex]

Simplify ,

. [tex]z=1.2359861303\approx1.24[/tex]

Hence, the observed z value would be 1.24 .

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