Question

A lathe is set to cut bars of steel into lengths of 6 centimeters. the lathe is considered to be in perfect adjustment if the average length of the bars it cuts is 6 centimeters. a sample of 121 bars is selected randomly and measured. it is determined that the average length of the bars in the sample is 6.08 centimeters. the population standard deviation is 0.44 centimeters. the correct null hypothesis for this problem is

Answer 1

The hypothesis testing for this problem is:
a. The hypothesis for this problem are:
Null: H0: μ=6
Alternative: Ha: μ≠6
 
b. Test
T-statistics = (6.08 - 6) / 0.44* √(121) = 2
 
c. P value = 0.047759
 
Since our p-value is smaller than the significant level of 0.05, we can say that we reject the null hypothesis.

Conclusion: there is enough evidence to say lathe is not in perfect adjustment.