Question

"Tongue Piercing May Speed Tooth Loss, Researchers Say" is the headline of an article. The article describes a study of 55 young adults with pierced tongues. The researchers found receding gums, which can lead to tooth loss, in 19 of the participants. (a) Construct a 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums. (Round your answers to three decimal places.)

Answer 1

The sample proportion of young adults with pierced tongues who have receding gums is:

$\hat{p}=\frac{x}{n}=\frac{19}{55}=0.345$

For 95% confidence level, critical value iof z is $z^*=1.96$. Therefore, a 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums is:

$\\\hat{p}\pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\= 0.345\pm 1.96\sqrt{\frac{0.345(1-0.345)}{55}}\\\\ =0.345\pm 1.96(0.0641)\\\\=0.345\pm 0.126 \ or \ {\color{Red} (0.219,0.471)}$