Chapter 4, Problem 4.6P

Interpretation Introduction

Interpretation:

The mean, standard deviation and 90% confidence interval has to be calculated.

Concept Introduction:

Mean:

The arithmetic mean (also called average) is the most commonly used measure of central tendency. It is calculated by summing the observed numerical values of a variable in a set of data and then dividing the total by the number of observations involved.

Computation of mean:

If ${\text{x}}_{\text{1}}{\text{,x}}_{\text{2}}\text{,}\mathrm{...}{\text{x}}_{\text{n}}$ be n values.

The mean value is calculated as,

    $\frac{{\displaystyle \sum _{\text{i=1}}^{\text{n}}{\text{x}}_{\text{i}}}}{\text{n}}$

Here, ${\displaystyle \sum _{\text{i=1}}^{\text{n}}{\text{x}}_{\text{i}}}$ is sum of all values and n is total number of values.

Standard deviation:

The standard deviation of a random variable X of size n is defined as,

  $s=\sqrt{\frac{{{\displaystyle \sum _{\text{i=1}}^{\text{n}}\left({\text{x}}_{\text{i}}-\overline{x}\right)}}^2}{\text{n-1}}}$, where ${\text{x}}_{\text{i}}$ is the i^th observation and $\overline{x}$ is the sample mean.

The standard deviation measures the absolute variability of a distribution.

The defined range of values that there is a specified probability that the value of a parameter lies with the range.