An appliance manufacturer claims to have developed a new toa

An appliance manufacturer claims to have developed a new toaster oven that consumes an average of no more than 250 W. From previous studies, it is believed that power consumption for toaster ovens is normally distributed with a standard deviation of 18 W. A consumer group suspects the actual average is more than 250 W. They take a sample of 16 toaster ovens and calculate the average consumption to be 260 W. The cut-off Watts at 2.5% level of significance is 258.82. The cut-off Watts at 1% level of significance is 260.485.

Answer the following questions:

1. In reality, suppose the average power consumption is 265 W. What is the Type II error when Type I error is set at 2.5%?

2. In reality, suppose the average power consumption is 265 W. What is the Type II error when Type I error is set at 1%?

3. Based on these calculations, what happens to Type II error if Type I error is lowered?

4. Based on these calculations, what happens to Type I error if Type II error is increased?

Answer Choices:

a) .1578
b) The error goes down
c) The error goes up
d) .0853

Please show how to solve these.

Solution