The city is considering the purchase of a different brand of

The city is considering the purchase of a different brand of lightbulbs for public buildings. The salesman claims that the new lightbulbs will last longer than the ones the city is currently using. Let represent the mean lifetime of the new lightbulbs, and suppose the mean lifetime of the bulbs currently being used is 10,000 hours, so that we can take the null hypothesis = 10, 000 (a) What alternate hypothesis would you take if the city is willing to purchase the new brand of lightbulbs unless they are actually worse than the old ones? (b) What would be the consequence of a Type I error? (c) What would be the consequence of a Type II error?

Solution

a)

H1 : the new brands of loghtbulbs are better than the old ones

b)

we would reject Ho, and we will select the bad brand of loghtbulbs as the good ones

c)

we would accept Ho, when this is false, so we will select the bad brand of loghtbulbs that are the old ones