Answer: (0.392, 0.668)
Step-by-step explanation:
Given : Sample size : n= 50
The proportion of successes : [tex]p=\dfrac{28}{50}=0.56[/tex]
Significance level : [tex]\alpha: 1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}=1.96[/tex]
The confidence interval for population proportion is given by :-
[tex]p\pm\ z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}\\\\=0.53\pm(1.96)\sqrt{\dfrac{0.53(1-0.53)}{50}}\\\\\approx0.53\pm0.138\\\\=(0.392,\ 0.668)[/tex]
Hence, the 95% confidence interval for the proportion of manufacturing companies that use six sigma is (0.392, 0.668).
