Capacitors for use in a Low pass filter application are supposed to have a mean capacitance ( Farads) greater than 100 Farads. Assume that the standard deviation of the resistances is 5 Farads....

Capacitors for use in a Low pass filter application are supposed to have a mean capacitance (Farads)
greater than 100 Farads. Assume that the standard deviation of the resistances is 5 Farads. Capacitances will be measured for a sample of capacitors, and a test of the hypothesis  will be made. Assume that in fact the true mean resistance is 101 .

1. If 100 resistors are sampled, what is the power of a test made at the 5% level?


2. How many resistors must be sampled so that a 5% level test has power 0.95?


3. If 100 resistors are sampled, at what level must the test be made so that the power is 0.90?


4. If 100 resistors are sampled, and the rejection region is
   >
   100.5, what is the power of the test?