10 A dental laboratory has developed a new type of band for children who wear braces. The new bands are designed to be more comfortable, look better, and it is hoped realign teeth more rapidly than the standard braces now in use. The laboratory conducts an experiment to compare the mean wearing times necessary to correct a specific type of misalignment using standard braces and using the new bands. Forty children are used in the study. Twenty are randomly assigned the standard braces and twenty the new bands. The number of days each child must wear the braces or bands is recorded. Data file: c09s02e01. (Assume that the distributions of number of days taken to align the teeth are normally distributed.) A. Is there sufficient evidence to conclude that the new bands do not have to be worn as long as the standard braces, on the average? Use 0.01 significance level. B. Define a Type I error in terms of this problem, and discuss the consequences of this error. If you were making the choice between standard braces and the new bands, what level of significance would you choose? Explain. C. Estimate the difference in mean wearing time between the braces and bands. Use 99% level of confidence