Question

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/underroot pq/n
Using the formula and data provided, what is the value of the z-test statistic?

Answer 1

0.68

Explanation:

The formula for z test is given above as:

z = p' - p/√(pq/n)

p' = sample proportion

= Number of infested samples(trees)/ Number of samples

p' = 127/1000 = 0.127

p = 12% = 0.12

q= 1 - 0.12 = 0.88

n = number of samples = 1000

z = 0.127 - 0.12/√(0.88 × 0.12/1000)

z = 0.007/√0.0001056

z = 0.007 /0.0102761861

z = 0.6811865737

Therefore, the z test statistic is approximately ≈ 0.68