A new machine is introduced into a production of something c

A new machine is introduced into a production of something called tutu. The machine has been tested 50 times throughout the first year of the production. It had average of producing 129 tutus per day with standard deviation of 12. The data for all the other machine indicate mean of 135 with standard deviation of 14. Should the new machine be replaced?

Solution

mean =129 abd s.d = 12.....
test H0: new machine mean =135 ag. less than 135..
Test statistic = (129 - 135)/ ( 12/ sqrt(50) = -3.535534...

p-value = 0.0004500014...df = 50-1 = 49....

which is less than our level of significance = 0.01..
so, we reject H0 and state that it should be replaced....