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A New Type of Band Has Been Developed for Children

question 61

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A new type of band has been developed for children who have to wear braces. The new bands are designed to be more comfortable, look better, and provide more rapid progress in realigning teeth. An experiment was conducted to compare the mean wearing time necessary to correct a specific type of misalignment between the old braces and the new bands. One hundred children were randomly assigned, 50 to each group. A summary of the data is shown in the table.
 Old Braces  New Bands xˉ410 days 380 days s41 days 65 days \begin{array} { c | r c } & \text { Old Braces } & \text { New Bands } \\\hline \bar { x } & 410 \text { days } & 380 \text { days } \\s & 41 \text { days } & 65 \text { days }\end{array}

How many patients would need to be sampled to estimate the difference in means to within 26 days with probability 99%?

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Definitions:

Lump Sum

A one-time transaction executed at a specific moment, rather than multiple transactions spread out over a period.

Rate Of Return

The profit or loss on an investment over a specified period, expressed as a percentage of the investment's initial cost.

Retirement

The phase of life when an individual stops working full-time, typically marked by reaching a certain age or financial stability.

College Education

Attaining higher education and academic degrees from colleges or universities.

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