Question

Chegg Detecting acid rain: power by hand. Even though software is used in practice to calculate power, doing the work by hand in a few examples will build your understanding of this concept. Find the power of the test in Exercise 15.41 for a sample of size n

Answer 1

Solution :

a). Standard error of sample mean =  $\frac{\sigma}{\sqrt n}$

                                                          $=\frac{0.5}{\sqrt{15}}$

                                                        = 0.1290994

The observed mean point be $\overline x$

Test statistics z = $\frac{\text{(observed mean - hypothesized mean)}}{\text{standard error}}$

                         $=\frac{\overline x -5}{0.1290994}$

For the left one sided test, critical value of z to reject $H_0 = -1.64$

We reject $H_0$ when test statics z < -1.64

b).  Value of  $\overline x$  z < -1.64

   $=\frac{(\overline x-5)}{0.1290994}$

  $=\overline x < 5-0.1290994 \times 1.64$

  $=\overline x < 4.78828$

∴ we reject $H_0$ when $\overline x < 4.78828$

c). The probability of rejecting $H_0$ when $\mu = 4.7$,

  $P(x$

                            $=P(z$

                           $=0.7517$