Please answer both parts a and b. Thank you in advance! Dental researchers have
ID: 3222500 • Letter: P
Question
Please answer both parts a and b. Thank you in advance!
Dental researchers have developed a new material for preventing cavities, a plastic sealant that is applied to the chewing surfaces of teeth. To determine whether the sealant is effective, it was applied in half of the teeth of each of twelve school-age children. The remaining teeth were untreated. After five years, the number of cavities in the sealant-coated teeth and the untreated teeth were counted. The results are given in the table below.
Notice that the difference is determined by taking the number of cavities in the untreated teeth minus the number of cavities in the sealant-coated teeth.
a) Are the samples independent or dependent? Explain.
b) A 95% confidence interval for the difference in mean number of cavities for untreated teeth and for sealant-coated teeth (untreated minus sealant-coated) is (0.12,2.21). Which of the following statements are correct? At least one is correct.
i. We are 95% confident that the mean number of cavities is between 0.12 and 2.21.
ii. We are 95% confident that the mean number of cavities in untreated teeth is between 0.12 and 2.21 larger than the mean number of cavities in sealant-coated teeth.
iii. At this confidence level, there is insufficient evidence to conclude that the mean number of cavities in sealant-coated teeth differs from the mean number of cavities in untreated teeth.
iv. We are 95% confident that the mean number of cavities differs from zero.
v. Since the confidence interval does not contain zero, it is impossible that the population mean number of cavities for sealant-coated teeth and the population mean number of cavities for untreated teeth are the same.
Circle the correct statement(s). You may include your reasoning below for possible partial credit in the case of a wrong answer.
Child 1 2 3 4 5 6 7 8 9 10 11 12 Mean St. Dev. Sealant-coated 2 1 0 3 1 0 1 2 1 0 1 2 1.17 0.94 Untreated 3 3 2 4 0 1 4 0 5 0 3 3 2.33 1.72 Difference 1 2 2 1 -1 1 3 -2 4 0 2 1 1.17 1.64Explanation / Answer
a) Are the samples independent or dependent?
Answer : Independent
b) A 95% confidence interval for the difference in mean number of cavities for untreated teeth and for sealant-coated teeth (untreated minus sealant-coated) is (0.12,2.21). Which of the following statements are correct? At least one is correct.
Answer : We are 95% confident that the mean number of cavities is between 0.12 and 2.21.