Question

5. A manufacturer must test that his bolts are 2.00 cm long when they come off the assembly line. He must recalibrate his machines if the bolts are too long or too short. After sampling 100 randomly selected bolts off the assembly line, he calculates the sample mean to be 1.90 cm. He knows that the standard deviation is 0.50 cm. Assuming a level of significance of 0.05, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines? Interpret the result.

Answer 1

H0: = 2

Ha: 2

Test Statistic :-
Z = ( X̅ - µ ) / ( σ / √(n))
Z = ( 1.9 - 2 ) / ( 0.5 / √( 100 ))
Z = -2
Test Criteria :-
Reject null hypothesis if | Z | > Z( α/2 )
Critical value Z(α/2) = Z( 0.05 /2 ) = 1.96
| Z | > Z( α/2 ) = 2 > 1.96
Result :- Reject null hypothesis

Conclusion - We have sufficient evidence to support the claim that the manufacturer needs to  

recalibrate the machines