Question

There are 300 welders employed at Maine Shipyards Corporation. A sample of 30 welders revealed that 18 graduated from a registered welding course. Construct the 95 percent confidence interval for the proportion of all welders who graduated from a registered welding course

Answer 1

Answer:  (0.4247,0.7753)

Step-by-step explanation:

Given : Sample size : n=30

Number of people graduated from a registered welding course =18

The probability of people graduated from a registered welding course :$p=\dfrac{18}{30}=0.6$

Significance level : $\alpha:1-0.95=0.05$

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

A confidence interval for population proportion is given by :-

$p \pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}\\\\=0.6\pm(1.96)\sqrt{\dfrac{0.6(1-0.6)}{30}}\\\\\approx0.6\pm0.1753\\\\=(0.4247,0.7753)$

Hence,  the 95 percent confidence interval for the proportion of all welders who graduated from a registered welding course = (0.4247,0.7753)