Chapter 4.4, Problem 6TY

Interpretation Introduction

Interpretation:

Whether the given two masses of nitrogen are significantly different or not has to be given.

Concept Introduction:

Comparing Replicate Measurements:

Standard deviations are Significantly Different:

When the standard deviations of two sets of measurements are significantly different, the equation for the t test is given as:

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

The degrees of freedom is given as:

$\begin{array}{l}\text{Degrees of freedom}\text{=}\frac{{(s_1^2/n_1+s_2^2/n_2)}^2}{\frac{{(s_1^2/n_1)}^2}{n_1-1}+\frac{{(s_2^2/n_2)}^2}{n_2-1}}\\ =\frac{{(u_1^2+u_2^2)}^2}{\frac{u_1^4}{n_1-1}+\frac{u_2^4}{n_2-1}}\end{array}$

To Give: Whether the given two masses of nitrogen are significantly different or not