Question

New heat lamps are reported to have the mean lifespan of 100 hours with a standard deviation of 15 hours. Before replacing their current lamp to the new heat lamps for the university, OSU decided to test whether the mean lifetime is equal to 100 or not by sampling 36 heat lamps. They turned them on and recorded the time, in hours, until each lamp failed. The sample provided a mean lifespan is 105.1 hours.

a) According to the Central Limit Theorem, the standard deviation of the distribution of the sample means is?

b) What is the approximate probability of observing a sample mean of 105.1 or more from the distribution of sample means, again assuming that the null hypothesis is true? (Use the 68-95-99.7 rule to approximate this probability. It may be helpful to sketch out the distribution)

Answer 1

a)

Answer: 2.500

b)

According to empirical rule, 95% data values lie between 95 and 105. That is area outside interval (95, 105) is 100% - 95% = 5%. This 5% area divided at both tails equally. That area right to 105 is

5%/ 2= 2.5%

Answer: 2.5% approximately