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An article claims that 12% of trees are infested by a bark beetle. A random sample of 1,000 trees were tested for traces of the infestation and found that 127 trees were affected.
z = p - p/p q/n
Using the formula and data provided, what is the value of the z-test statistic?

Answer :

JeanaShupp

Answer: 0.6812

Step-by-step explanation:

Let p be the population proportion of trees are infested by a bark beetle.

As per given: p= 12%= 0.12

Sample size : n= 1000

Number of trees affected in sample = 1000

Sample proportion of trees are infested by a bark beetle. = [tex]\hat{p}=\dfrac{127}{1000}=0.127[/tex]

Now, the z-test statistic : [tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]

So, [tex]z=\dfrac{0.127-0.12}{\sqrt{\dfrac{0.12\times 0.88}{1000}}}[/tex]

[tex]z=\dfrac{0.007}{\sqrt{\dfrac{0.1056}{1000}}}\\\\\\=\dfrac{0.007}{\sqrt{0.0001056}}\\\\\\=\dfrac{0.007}{0.010276}\approx0.6812[/tex]

Hence, the value of the z-test statistic = 0.6812 .

Answer:

0.70

Step-by-step explanation:

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