Answer to Question #244675 in Statistics and Probability for blossomqt

Question

A builder claims that bidets are installed in more than 50% of all homes being constructed today in suburban Lapu-lapu. Would you agree with this claim if a random survey of new homes in this city showed that 54 out of 150 had bidets installed? Use a 0.05 level of significance.

Answer 1

Solution:

Null hypothesis, H₀ : $p=0.50$

Alternate hypothesis, H₁ : $p>0.50$

$\alpha=0.05$, two -tailed test.

Critical value$=z_{\alpha/2}=1.96$

Test statistic$=z=\dfrac{\hat p-p}{\sqrt{pq/n}}\sim N(0,1)$

$\hat p=54/150=0.36$

Then, $z=\dfrac{0.36-0.50}{\sqrt{0.50\times0.50/150}}=-3.43$

Thus, we have enough evidence to reject the null hypothesis.

So, $p>0.50$.