# Mathematical Statistics and Data Analysis - Solutions

### Chapter 7, Survey Sampling

#### (b)

We have $\, P(\left\vert \bar X - \mu \right\vert > \delta) \approx l \,$

We shall first find an expression to compute $\, \delta \,$

Thus we can compute $\, \delta \,$ as:

$\, \sigma_{\bar X} \,$ can be computed using the formuale $\, \frac {\sigma} {\sqrt{n} } \sqrt{ 1 - \frac{n-1} {N-1} } \,$

We have $\, \sigma = 589.716 \,$ from the example quoted in the problem. To compute $\, \Phi^{-1} \,$, we can use the normal tables given in the end of the book.

Now we just need to insert the values into the formulae to compute $\, \delta \,$

$\, n=20 \,$ $\, n=40 \,$ $\, n=80 \,$
$\, l=0.10 \,$ $\, 211.583 \,$ $\, 145.650 \,$ $\, 96.918 \,$
$\, l=0.50 \,$ $\, 87.4677 \,$ $\, 60.2 \,$ $\, 40.06288 \,$
$$\tag*{\blacksquare}$$