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 17 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

Solution :

Given that,

n = 51

x = 17

= x / n = 17/51 = 0.333

1 - = 1 - 0.667

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error (E) = Z _{/ 2} * [ * (1 - ) / n]

= 1.96 * [(0.333 * 0.667) / 51]

= 0.066

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.333 - 0.066 < p < 0.333 + 0.066

0.267 < p < 0.400

(0.267, 0.400)