Chapter 4, Problem 4.18P

Interpretation Introduction

Interpretation:

Whether the given sets of measurements gives equivalent results are not has to be explained using spreadsheet calculations.

Concept Introduction:

Comparison of Standard Deviation with F Test:

For the comparison of mean values of two sets of measurements, we decide whether the standard deviations of the two sets are “statistically different”. This is done by F test.

The F test with quotient F is given as:

${\text{F}}_{\text{calculated}}=\frac{s_1^2}{s_2^2}$

Where, $s_1$ and $s_2$ are standard deviations for the set of measurements using original instrument and substitute instrument.

If ${\text{F}}_{\text{calculated}}>{\text{F}}_{\text{table}}$ , then the difference is significant.

Degrees of Freedom:

For a n set of measurement, the degrees of freedom will be $(n-1)$

Comparing replicate measurements:

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 given sets of measurements gives equivalent results using spreadsheet calculations.