Question

A dentist was interested in the effectiveness of a new toothpaste. A group of N=1000 schoolchildren participated in a study. Pre-study records showed there was an average of 2.2 cavities every six months for the group. After three months of the study, the dentist sampled n=10 children to determine how they were progressing on the new toothpaste. Using the data in the accompanying table, estimate the total number of cavities for the entire group. Place a bound on the error of estimation. Based on the data, do you think the dentist can say the toothpaste didn’t change the average number of cavities of 2.2? Determine the sample size required to estimate mean number of cavities, with a bound on the error of estimation of magnitude B = 0.25.

Child                                  Number of cavities in three month period

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1                                                              0

2                                                              4

3                                                              2

4                                                              3

5                                                              2

6                                                              0

7                                                              3

8                                                              4

9                                                              1

10                                                            1

Answer 1