The two samples analyzed in Example 14.7 are known to contain the following

Question

The two samples analyzed in Example 14.7 are known to contain the following concentrations of cholesterol.

[latex]\mu_{ ext {samp 1 }}=248.3~ \mathrm{mg} / 100 \mathrm{~mL} \quad \mu_{ ext {samp 2 }}=247.6~ \mathrm{mg} / 100 \mathrm{~mL}[/latex]

Determine if there is any evidence for a systematic error in the method at the 95% confidence level.

Accepted Answer

Using the data from Example 14.7 and the true values for the samples, we know that [latex]s_{\mathrm{T}}[/latex] is 13.3 , and

[latex] \begin{gathered} \bar{T}=\bar{X}_{ ext {samp } 1}+\bar{X}_{ ext {samp 2 }}=245.9+243.5=489.4 \ \mu_{ ext {tot }}=\mu_{ ext {samp } 1}+\mu_{ ext {samp 2 }}=248.3+247.6=495.9 \end{gathered} [/latex]

Substituting these values into equation 14.20

[latex]t_{\mathrm{exp}}\,=\,{\frac{\left|\overline{{{T}}}\,-\,\mu_{\mathrm{tot}} ight|\sqrt{n}}{s_{\mathrm{T}}\sqrt{2}}}\,.[/latex] (14.20)

gives

[latex]t_{\exp }=\frac{|489.4-495.9| \sqrt{10}}{13.3 \sqrt{2}}=1.09[/latex]

This value for [latex]t_{\exp }[/latex] is smaller than the critical value of 2.26 for [latex]t(0.05,9)[/latex]. Thus, there is no evidence for a systematic error in the method at the [latex]95 \%[/latex] confidence level.

Question 14.8: The two samples analyzed in Example 14.7 are known to contai...

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