Question

11) In the past, the mean battery life for a certain type of flashlight battery has been 8.8 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean battery life has increased as a result. The hypotheses are: H0 : 4 = 8.8 hours H4> 8.8 hours a) Explain the result of a Type I erro b) Explain the result of a Type II error.

Answer 1

(a)

Here the null hypothesis is that the population mean battery life for a certain type of battery is 8.8 hours. Type I error is defined as the error commited in rejecting the null hypothesis when it is true. Here Type I error would be if it is concluded that the population mean battery life for a certain type of battery is more than 8.8 hours when it is actually 8.8 hours.

(b)

Here the null hypothesis is that the population mean battery life for a certain type of battery is 8.8 hours. Type II error is defined as the error commited in accepting the null hypothesis when it is false. Here type II error would be if it is concluded that the population mean battery life for a certain type of battery is 8.8 hours when it is actually more than 8.8 hours.

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