Question

1. Find the data for the problem in the first worksheet named LightbulbLife of the data file. It gives the data on the lifetime in hours of a sample of 100 lightbulbs. The company manufacturing these bulbs wants to know whether it can claim that its lightbulbs typically last more than 1000 burning hours. So it did a study.
   1. Identify the null and the alternate hypotheses for this study.
   2. Can this lightbulb manufacturer claim at a significance level of 5% that its lightbulbs typically last more than 1000 hours? What about at 1%? Test your hypothesis using both, the critical value approach and the p-value approach. Clearly state your conclusions.
   3. Under what situation would a Type-I error occur? What would be the consequences of a Type-I error?
   4. Under what situation would a Type-II error occur? What would be the consequences of a Type-II error?

Answer 1

Sample size = 100

(a) Null hypothesis : H0 : μ = 1000 Hours

Alternative Hypothesis : Ha : μ > 1000 hours

(b) Data is not associated with the problem so can't solve the problem number (b)

(c) Here type - I error occur when we reject the null hypothesis when it is true that means We will conclude that the mean lifetime of the bulb is greater than 1000 hours when in true it is 1000 hours. Here the consequences of type -I error is we could have purchased bulbs assuming the bulbs have larger mean hours but in truth it is not. It will be less cost effective.

(d) Here type - II error occur when we fail to reject the null hypothesis when it is false that means We will conclude that the mean lifetime of the bulb is not greater than 1000 hours when in true it is more than 1000 hours. Here the consequences of type -II error is we would not purchased bulbs assuming the bulbs have 1000 hours but in truth it is more than that. It would cost us a lot.