One article describes a study of 51 young adults with pierced tongues. The resea

Question

One article describes a study of 51 young adults with pierced tongues. The researchers found receding gums, which can lead to tooth loss, in 23 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.)

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

the sample is a random sample

the sample is voluntary

the sample size is large

the sample is independent

Explanation / Answer

given that p = 23/51 = 0.45 , also we see that the z value for 95% CI is 1.96 from the z table

now we know that the CI of proportions is given as

p +- z*sqrt(p*(1-p)/n)

putting the values in the above equation ad sloving them we get

0.45 +- 1.96* sqrt(0.45*0.55/51) , we get the confidence intervals as

0.313 and 0.586

all the assumptions are needed to perform the z confidence interval

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