Question

"Tongue Piercing May Speed Tooth Loss, Researchers Say" is the headline of an article. The article describes a study of 51 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.) ( .138 Incorrect: Your answer is incorrect. , .503 Incorrect: Your answer is incorrect. )

Answer 1

Answer:

The 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums is (0.24, 0.506).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$, and a confidence level of $1-\alpha$, we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$.

For this problem, we have that:

$n = 51, \pi = \frac{19}{51} = 0.373$

95% confidence level

So $\alpha = 0.05$, z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$, so $Z = 1.96$.

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.373 - 1.96\sqrt{\frac{0.373*0.627}{51}} = 0.24$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.373 + 1.96\sqrt{\frac{0.373*0.627}{51}} = 0.506$

The 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums is (0.24, 0.506).