Question

jamestown steel company manufactures and assembles desks and other office equipment. The weekly production of the model A325 desk at the Fredonia Plant follows the normal probability distribution with a mean of 200 and a standard deviation of 16. Recently, new production methods have been introduced and new employees hired. The VP of manufacturing would like to investigate whether there has been a change in the weekly production of the Model A325 desk. A sample from last year's weekly production yielded a mean number of desks produced of 203.5.For a 0.01 significance level, what is the critical value?

a. 2.576

b. 2.326

c. 1.96

d. 1.645

Answer 1

Solution:
Given in the question
The VP of manufacturing would like to investigate whether there has been a change from 200 in the weekly production of the Model A325 desk so null hypothesis and alternate hypothesis can be written as
Null hypothesis H0: = 200
Alternate hypothesis Ha: 200
Sample mean = 203.5
Population standard deviation = 16
Here we will use standard normal distribution and this is two-tailed tests
at alpha or level of significance = 0.01
alpha/2 = 0.005 for lower tailed, from Z table we found Z-critical value = -2.576
alpha/2 = 0.995 for upper tailed, from Z table we found Z-critical value = +2.576
So its correct answer is A. i.e. 2.576