One article describes a study of 54 young adults with pierced tongues. The resea

Question

One article describes a study of 54 young adults with pierced tongues. The researchers found receding gums, which can lead to tooth loss, in 24 of the participants.

(a) Construct a 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums. (Use Table 3 in Appendix A. Give the answer to three decimal places.)
(  ,  )

(b) What assumptions must be made for use of the z confidence interval to be appropriate? (Select all that apply.)

the sample size is largethe sample is independentthe sample is voluntarythe sample is a random sample

Explanation / Answer

here estimated proportion p=24/54 =0.4444

std error =(p(1-p)/n)1/2 =0.0676

for 95% confidence level; z=1.96

therefore 95% confidence interval = p -/+ z*std error =0.3119 ; 0.5770

b)assumptions made for use of z confidence interval:

the sample size is large and the sample is a random sample.

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