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Determine from the graph whether the function has any absolute extreme values on $[a, b] .$ Then explain how your answer is consistent with Theorem 1.
What are the properties of the $t$ distribution?
What is meant by degrees of freedom?
Find the values for each.$$\begin{array}{l}{\text { a. } t_{\alpha / 2} \text { and } n=18 \text { for the } 99 \% \text { confidence interval for }} \\ {\text { the mean }} \\ {\text { b. } t_{\alpha / 2} \text { and } n=23 \text { for the } 95 \% \text { confidence interval for }} \\ {\text { the mean }} \\ {\text { c. } t_{\alpha / 2} \text { and } n=15 \text { for the } 98 \% \text { confidence interval for }} \\ {\text { the mean }} \\ {\text { d. } t_{\alpha / 2} \text { and } n=10 \text { for the } 90 \% \text { confidence interval for }} \\ {\text { the mean }} \\ {\text { e. } t_{\alpha / 2} \text { and } n=20 \text { for the } 95 \% \text { confidence interval for }} \\ {\text { the mean }}\end{array}$$
When should the $t$ distribution be used to find a confi-dence interval for the mean?
Digital Camera Prices The prices (in dollars) for aparticular model of digital camera with 18.0 megapixelsand a $f / 3.5-5.6$ zoom lens are shown here for 10randomly selected online retailers. Estimate thetrue mean price for this particular model with $95 \%$confidence.$$999 \quad 1499 \quad 1997 \quad 398 \quad 591 \quad 498 \quad 798 \quad 849 \quad 449 \quad 348$$
