Question

In Exercise 9-20, find the boundary of the critical region if the type I error probability is

9-20 A manufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally distributed with standard deviation 0.25 volt, and the manufacturer wishes to test volts, using n = 8 units.

Answer 1

(a) Let denote the critical values.

The distribution of the sample mean is approximately normal with the mean and the standard deviation

The z-values that correspond to the critical values are

Since, . Therefore,

Using the Cumulative Standard Normal Distribution table we find that and. Therefore,

Therefore, the acceptance region is

.

(b) For we have. Therefore,

Using the Cumulative Standard Normal Distribution table we find that and. Therefore,

Therefore, the acceptance region is

.

(c) Since n = 16, we have

The z-values that correspond to the critical values are

Since,. Therefore,

Using the Cumulative Standard Normal Distribution table we find that and. Therefore,

Therefore, the acceptance region is

.

(d) For we have . Therefore,

Using the Cumulative Standard Normal Distribution table we find that and. Therefore,

Therefore, the acceptance region is

.