Chapter 4, Problem 4.20P

Interpretation Introduction

Interpretation:

The concentration of $\text{HCl}$ is measured by titrating with different indicators.

Whether the difference between the indicators $1\text{ and 2}$, indicators $2\text{ and 3}$ are significant at the $95\%$ confidence level has to be given.

Concept Introduction:

Comparing replicate measurements:

When the two standard deviations are not significantly different from each other, the equation used is:

$\begin{array}{l}t\text{ test for comparison of means: }\\ t=\frac{\left|\overline{x_1}-\overline{x_2}\right|}{\sqrt{(s_{\text{pooled}})}}\sqrt{\frac{n_1{n}_2}{n_1+n_2}}(\text{since }{s}_{\text{pooled}}=\sqrt{\frac{s_1^2(n_1-1)+s_2^2(n_2-1)}{n_1+n_2-2}})\end{array}$

When the standard deviations of two sets of measurements are significantly different, the equations used are:

$\begin{array}{l}{t}_{\text{calculated}}=\frac{\left|\overline{x_1}-\overline{x_2}\right|}{\sqrt{(s_1^2/n_1+s_2^2/n_2)}}\\ \text{Degrees of freedom}\text{=}\frac{{(s_1^2/n_1+s_2^2/n_2)}^2}{\frac{{(s_1^2/n_1)}^2}{n_1-1}+\frac{{(s_2^2/n_2)}^2}{n_2-1}}\\ =\frac{{(u_1^2+u_2^2)}^2}{\frac{u_1^4}{n_1-1}+\frac{u_2^4}{n_2-1}}\end{array}$

To Give: Whether the difference between the indicators $1\text{ and 2}$, indicators $2\text{ and 3}$ are significant at the $95\%$ confidence level