Question 974101
Sample Size: *[Tex \LARGE n = 5]


I used a calculator to compute the following
Sample Mean: *[Tex \LARGE \bar{x} = 44.8]
Sample Standard Deviation: *[Tex \LARGE s = 6.7602] (approximate)


Using a <a href="http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf">t-table</a>, with degrees of freedom = df = n-1 = 5-1 = 4, we find that the critical t value at 95% confidence is approximately *[Tex \LARGE t_c = 2.776]

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Margin of Error (E)


*[Tex \LARGE E = t_c*\frac{s}{\sqrt{n}}]


*[Tex \LARGE E = 2.776*\frac{6.7602}{\sqrt{5}}]


*[Tex \LARGE E = 8.3926]

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Lower Limit L


*[Tex \LARGE L = \bar{x}-E = 44.8 - 8.3926 = 36.4074]


Upper Limit U


*[Tex \LARGE U = \bar{x}+E = 44.8 + 8.3926 = 53.1926]


The 95% confidence interval for the population mean of the ages is *[Tex \LARGE (L,U) = (36.4074,53.1926)]


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