Question

In order for a kitchen appliance to be considered "green" it should draw less than 250 watts. An appliance manufacturer claims to have developed a new "green" 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 20 toaster ovens and calculate the average consumption to be 260 W. Design and run a test with α = .06 to see if the consumer groups suspicions are justified.

Calculate the probability of a type two error, for the test above If the actual mean power usage of the new oven is 251 watts.

Answer 1

Note that the claim made is that the average power consumption is greater than 250W. So, its an upper tailed test. And as we are given the population standard deviation, so we would use a Z-test.

ltelna Test statistic-ブエーーーー う 260-250-2.48H 5 2 18 冰 研 an utpek tuled .test, do:. p-valueP (z 21845)0.0065 o tie Cenlude het the tooster Consunmes et Ho and on aucenge mete tarn So andus an's o. 0 6 PC2(シ555 Bruse yt ss when ur toid to get we tuoul

So,P(z555) o-94 So, tue Can it In o 1.555 vticat 250 nas ue haue a samgle mean ess tan 256. 2583. c, PC x < 256.2588| 시드251 618 - Pz 266 2588-25 0.909