Question

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. Answer the following questions:
a. Would you reject the Null at 1% level of significance?
b. Would you say the toaster oven consumes more than 250 W of power if you are willing to commit a Type 1 Error of 2.5%?
c. What is the cut-off Watts at 2.5% level of significance?
d. 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%?
e. What is the cut-off Watts at 1% level of significance?
f. In reality, suppose the average power consumption is 265 W. What is the Type II error when Type I error is set at 1%?
g. Based on these calculations, what happens to Type II error if Type I error is lowered?
h. Based on these calculations, what happens to Type I error if Type II error is increased?

Answer 1

Answer:

a. No the null hypothesis cannot be rejected at  1% level of significance as the calculated value of z= 2.222 which lies with in 2.333

b. Yes for the  Type 1 Error of 2.5% we say the toaster oven consumes more than 250 W of power because the calculated value 2.22 lies outside the region for 1.96

c. The cut-off at 2.5% level of significance is 258.82 W.

d. 0.85 is the area for Type 2 error.

e. The cut-off at 1% level of significance is 260.485W.

f.  0.154 is the area for Type 2 Error

g. The  Type 2 Error is increased when Type 1 Error is decreased.

h. The  Type 1 Error is decreased when Type 2 Error is increased .

Step-by-step explanation:

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