Chapter 4.2, Problem 4TY

Interpretation Introduction

Interpretation:

Whether the difference in standard deviations of the two sets each of which have 13 replications is significant or not has to be explained.

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. Always consider larger standard deviation in the numerator.

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 $(n-1)$

To Explain: Whether the difference in standard deviations of the two sets each of which have 13 replications is significant or not