Answer to Question #350852 in Statistics and Probability for Mark

Question

Problem 2

The Senior High School researchers claim that 20% of Senior High School male students have tried smoking cigarette. After collecting 150 random samples, they found 40 of them have tried smoking cigarette.

Hypothesized proportion (p̂), th value of q, and finally the value of z.

*

p̂ = 0.27, q = 0.9, z = 2.05

p̂ = 0.27, q = 0.8, z = 2.14

p̂ = 0.27, q = 0.8, z = 2.0412

p̂ = 0.33, q = 0.7, z = 0.8

Answer 1

$$\hat{p}=\dfrac{x}{n}=\dfrac{40}{150}=\dfrac{4}{15}\approx0.27$$

$$q=1-p=1-0.2=0.8$$

The z-statistic is computed as follows:

$$z=\dfrac{\hat{p}-p_0}{\sqrt{\dfrac{p_0(1-p_0)}{n}}}=\dfrac{40/150-0.2}{\sqrt{\dfrac{0.2(1-0.2)}{150}}}=2.0412$$

$p̂ = 0.27, q = 0.8, z = 2.0412$