Answer to Question #92331 in Statistics and Probability for mimi

Question

Dyson Company in Senai Johor plans to produce a new hair product known as Dyson Supersonic. The suppliers for the company are Company A and Company B found that 1% and 2% defective of 200 and 300 items respectively. Arrange appropriate hypothesis testing to investigate whether Company B is better by using a 0.05 level of significance.

Answer 1

Null hypothesis $H_0:\;p_1=p_2$

Alternative hypothesis $H_a:\;p_1< p_2$

Pooled sample proportion: $E=mc^2p=\frac{p_1n_1+p_2n_2}{n_1+n_1}=\frac{0.01*200+0.02*300}{200+300}=0.016$

Test statistic: $z=\frac{p_1-p_2}{\sqrt{p(1-p)(\frac{1}{n_1}+\frac{1}{n_2})}}=-0.87.$

P-value: $p=0.191.$

Since the P-value is greater than 0.05, reject the null hypothesis.