Answer to Question #339924 in Statistics and Probability for None

Question

XY company claims that their lightbulb can last for 6,000 hours. 24 samples were tested, and the average lifespan is 5600 hours with a standard deviation of 300. is there a convincing evidence that the XY lightbulbs cannot last for 6,000 hours?

a) formulate the null and alternative hypothesis

b) determine what test statistic to use

c) calculate the test statistic value

Answer 1

a) The following null and alternative hypotheses need to be tested:

$H_0:\mu\ge 6000$

$H_a:\mu<6000$

b) This corresponds to a left-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.

c) The t-statistic is computed as follows:

$$t=\dfrac{\bar{x}-\mu}{s/\sqrt{n}}=\dfrac{5600-6000}{300/\sqrt{24}}=-6.5320$$