Answer to Question #350854 in Statistics and Probability for Cess

Question

Problem 3

A teacher wants to test his assumption that less than 30% of the Senior High School students like research class. After randomly collecting 150 samples, he found out that only 50 students like their research class.

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

$$\hat{p}=\dfrac{x}{n}=\dfrac{50}{150}=\dfrac{1}{3}\approx0.33$$ $$q=1-p=1-0.3=0.7$$

The z-statistic is computed as follows:

$$z=\dfrac{\hat{p}-p_0}{\sqrt{\dfrac{p_0(1-p_0)}{n}}}=\dfrac{50/150-0.3}{\sqrt{\dfrac{0.3(1-0.3)}{150}}}=0.89$$

$p̂ = 0.33, q = 0.7, z = 0.8$