A metallurgist has invented a new tungsten alloy for use in the filaments of lightbulbs that is supposed to burn brighter with the use of less energy....

A metallurgist has invented a new tungsten alloy for use in the filaments of lightbulbs that is supposed to burn brighter with the use of less energy. A company investigates that potential cost of producing the new type of bulb and decides that production would be economically feasible if the bulbs would last an average of longer than 2000 hours and continuous usage. 25 of the new bulbs are tested and found to last an average of 2240 hours with a standard deviation of 600 hours. Is this strong evidence that the average life of all such bulbs is higher than 2000 hours? Translate this into a statistical hypothesis test problem and carry out the test. Be sure to give the null and alternative hypothesis, the value of the test statistic, the P value, and your conclusions.