Question

One article describes a study of 81 randomly selected young adults with pierced tongues. The researchers found receding gums, which can lead to tooth loss, in 25 of the participants.

(a) Construct a 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums. (Don’t forget to check all conditions necessary to your construction!)

(b) Write a sentence in which you correctly interpret the confidence interval you created.

(c) Would the interval you found in (a) have been wider, narrower, or the same width if only 60 young adults had been sampled?

Answer 1

a)

Sample proportion = 25 / 81 = 0.309

95% confidence interval for p is

- Z/2 * sqrt [ ( 1 - ) / n ] < p < + Z/2 * sqrt [ ( 1 - ) / n ]

0.309 - 1.96 * sqrt [ 0.309 ( 1 - 0.309) / 81] < p < 0.309 + 1.96 * sqrt [ 0.309 ( 1 - 0.309) / 81]

0.208 < p < 0.410

95% CI is ( 0.208 , 0.410 )

b)

Interpretation - We are 95% confident that the true proportion of young adults with pierced

tongues who have receding gums is between 0.208 and 0.410

c)

If sample size had 60 (that is less than previous 81) ,

the confidence interval would be wider (since margin of error increases)