Question

1. "Tongue Piercing May Speed Tooth Loss, Researchers Say" is the headline of an article. The article describes a study of 47 young adults with pierced tongues. The researchers found receding gums, which can lead to tooth loss, in 16 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.)
(  ,  )

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

The sample size is large.

The sample is voluntary

.The sample is independent

.The sample is a random sample.

2. Acrylic bone cement is sometimes used in hip and knee replacements to fix an artificial joint in place. The force required to break an acrylic bone cement bond was measured for six specimens under specified conditions, and the resulting mean and standard deviation were 304.89 Newtons and 41.07 Newtons, respectively. Assuming that it is reasonable to assume that breaking force under these conditions has a distribution that is approximately normal and using 95% confidence level, estimate the true average breaking force f for acrylic bone cement under the specified conditions. (Use Table 3 in Appendix A. Round your answer to the nearest whole number.)
(. ≤ f ≤. )

Answer 1

1. n = 47, x = 16

p̅ = x/n = 0.3404

a) 95% Confidence interval :

At α = 0.05, two tailed critical value, z_c = NORM.S.INV(0.05/2) = 1.960

Lower Bound = p̄ - z_c*√( p̄ *(1- p̄ )/n) = 0.3404 - 1.96 *√(0.3404*0.6596/47) = 0.205

Upper Bound = p̄ + z_c*√( p̄ *(1- p̄ )/n) = 0.3404 + 1.96 *√(0.3404*0.6596/47) = 0.476

(b) Assumptions:

• The sample size is large.
• The sample is independent
• The sample is a random sample.

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2.

x̅ = 304.89, s = 41.07, n = 6

95% Confidence interval :

At α = 0.05 and df = n-1 = 5, two tailed critical value, t-crit = T.INV.2T(0.05, 5) = 2.571

Lower Bound = x̅ - t-crit*s/√n = 304.89 - 2.571 * 41.07/√6 = 262

Upper Bound = x̅ + t-crit*s/√n = 304.89 + 2.571 * 41.07/√6 = 348

262 < f < 348