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Question

# Construct the indicated confidence interval for the population mean$\mu$using the t-distribution.$c = 0.99 , \overline { x } = 24.7 , s = 4.6 , n = 50$

Solution

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Determine the t-value by looking in the row starting with degrees of freedom $n-1=50-1=49$ in table 5:

$t_{c}=t_{0.99}=2.678$

The confidence interval is:

$\overline{x}-t_{\alpha/2}\cdot \dfrac{s}{\sqrt{n}}\text{ to }\overline{x}+t_{\alpha/2}\cdot \dfrac{s}{\sqrt{n}}$

Fill in the known values:

$24.7-2.678\cdot \dfrac{4.6}{\sqrt{50}}\text{ to }24.7+ 2.678\cdot \dfrac{4.6}{\sqrt{50}}$

Simplify:

$22.958\text{ to }26.442$

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