In the past, the mean running time for a certain type offlashlight battery has b

Question

In the past, the mean running time for a certain type offlashlight battery has been 9.3 hours. The manufacturer hasintroduced a change in the production method and wants to perform ahypothesis test to determine whether the mean running time hasincreased as a result. Explain the result of a Type I error. A) The manufacturer will decide the mean battery life is lessthan 9.3 hours when in fact it is greater than 9.3 hours. B) The manufacturer will decide the mean battery life isgreater than 9.3 hours when in fact it is greater than 9.3hours. C) The manufacturer will decide the mean battery life isgreater than 9.3 hours when in fact it is not more than 9.3hours. D) The manufacturer will decide the mean battery life is lessthan 9.3 hours when in fact it is less than 9.3 hours. E) The manufacturer will decide the mean battery life is nomore than 9.3 hours when in fact it is greater than 9.3hours. In the past, the mean running time for a certain type offlashlight battery has been 9.3 hours. The manufacturer hasintroduced a change in the production method and wants to perform ahypothesis test to determine whether the mean running time hasincreased as a result. Explain the result of a Type I error. A) The manufacturer will decide the mean battery life is lessthan 9.3 hours when in fact it is greater than 9.3 hours. B) The manufacturer will decide the mean battery life isgreater than 9.3 hours when in fact it is greater than 9.3hours. C) The manufacturer will decide the mean battery life isgreater than 9.3 hours when in fact it is not more than 9.3hours. D) The manufacturer will decide the mean battery life is lessthan 9.3 hours when in fact it is less than 9.3 hours. E) The manufacturer will decide the mean battery life is nomore than 9.3 hours when in fact it is greater than 9.3hours.

Explanation / Answer

Type I error is the rejection of a true null hypothesis. (In otherwords, accepting a false alternate hypothesis). In the context ofthis question, the Type I error is commited in answer C: The manufacturer will decide themean battery life is greater than 9.3 hours when in fact it is notmore than 9.3 hours. This is correct because the nullhypothesis woulde be that the true battery life is still 9.3 hours,but if the manufacturer rejects the null and concludes thatthe mean life is greater than 9.3 hours, that would be rejecting atrue null hypothesis, or Type I error.

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