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

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

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{(\pi(1-\pi))/(n)}`

In which

z is the zscore that has a pvalue of
`1 - (\alpha)/(2)`.

For this problem, we have that:

`n = 51, \pi = (19)/(51) = 0.373`

95% confidence level

So
`\alpha = 0.05`, z is the value of Z that has a pvalue of
`1 - (0.05)/(2) = 0.975`, so
`Z = 1.96`.

The lower limit of this interval is:

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

The upper limit of this interval is:

`\pi + z\sqrt{(\pi(1-\pi))/(n)} = 0.373 + 1.96\sqrt{(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).