Answer to Question #350851 in Statistics and Probability for Princess

Question

Problem 1

A student researcher claims that 8% of the Junior High School completers will enroll in private Senior High Schools. To test this claim, he collected sufficient samples randomly and found out that 85 out of 380 Junior High School completers are planning to enroll in private Senior High Schools.

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

*

p̂ = 0.43, q = 0.98, z = 20.45

p̂ = 0.22, q = 0.42, z = 10.45

p̂ = 0.60, q = 0.92, z = 11.45

p̂ = 0.22, q = 0.92, z = 10.05

p̂ = 0.22, q = 0.92, z = 10.324

Answer 1

$$\hat{p}=\dfrac{x}{n}=\dfrac{85}{380}\approx0.22$$ $$q=1-p=1-0.08=0.92$$

The z-statistic is computed as follows:

$$z=\dfrac{\hat{p}-p_0}{\sqrt{\dfrac{p_0(1-p_0)}{n}}}=\dfrac{85/380-0.08}{\sqrt{\dfrac{0.08(1-0.08)}{380}}}=10.324$$

$p̂ = 0.22, q = 0.92, z = 10.324$