Question

An average light bulb manufactured by the Acme Corporation lasts 300 days with a standard deviation of 50 days (this distribution is normally distributed). My new friend has started to manufacture more energy efficient light bulbs, but he is not sure if he has a good bulb. He gave me 27 bulbs, and thinks that his bulbs last 310 days. What would power be if I tested his 27 bulbs, using a two-tailed, alpha=.05 test? What is the critical value for the null hypothesis true graph?

Options: z = 1.96 z=-1.96 t=-1.706 t=+1.706 z = 1.645 z= -1.645 there is no critical value for this problem t=2.056 t=-2.056

Answer 1

Solution :

Given that,

Population mean = = 310

Sample mean = = 300

Sample standard deviation = s = 50

Sample size = n = 27

Level of significance = = 0.05

This is a two tailed test.

Therefore, the standard deviation is unknown, then we use t distribution.

Critical value of  the significance level is α = 0.05, and the critical value for a two-tailed test is

= 2.056

The answer is t = 2.056