UCLA

[logistic_guy]

A \(\displaystyle \text{UCLA}\) researcher claims that the life span of mice can be extended by as much as \(\displaystyle 25\%\) when the calories in their diet are reduced by approximately \(\displaystyle 40\%\) from the time they are weaned. The restricted diet is enriched to normal levels by vitamins and protein. Assuming that it is known from previous studies that \(\displaystyle \sigma = 5.8\) months, how many mice should be included in our sample if we wish to be \(\displaystyle 99\%\) confident that the mean life span of the sample will be within \(\displaystyle 2\) months of the population mean for all mice subjected to this reduced diet?

 

[khansaheb]

A \(\displaystyle \text{UCLA}\) researcher claims that the life span of mice can be extended by as much as \(\displaystyle 25\%\) when the calories in their diet are reduced by approximately \(\displaystyle 40\%\) from the time they are weaned. The restricted diet is enriched to normal levels by vitamins and protein. Assuming that it is known from previous studies that \(\displaystyle \sigma = 5.8\) months, how many mice should be included in our sample if we wish to be \(\displaystyle 99\%\) confident that the mean life span of the sample will be within \(\displaystyle 2\) months of the population mean for all mice subjected to this reduced diet?

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[Agent Smith]

[imath]\mu = \overline x \pm z^* \frac{\sigma_x}{\sqrt n}[/imath]

[imath]\pm 2 = \pm z^* \frac{\sigma_x}{\sqrt n}[/imath]

[imath]2 = 2.57 \times \frac{5.8}{\sqrt n}[/imath]

[imath]n \approx 56[/imath]