Question

Suppose you are determining whether the depth of groves cut into aluminum by a milling machine is equal to 1.7 mm. You cut 14 groves, then measure the depth of each one. With these measurements, you perform a statistical hypothesis test to determine whether the groove depth is equal to 1.7 mm. Which of the following tests would you use?

1. This one-sided test:
H0: μ = 1.7 mm
H1: μ < 1.7 mm
2. This one-sided test:
H0: μ = 1.7 mm
H1: μ > 1.7 mm
3. This two-sided test:
H0: μ = 1.7 mm
H1: μ ≠ 1.7 mm
4. This two-sided test:H0: μ > 1.7 mm
H1: μ = 1.5 mm

Answer 1

For this case we want to check if the true mean for the depth of groves cut into aluminium by a machine is equal to 1.7 (null hypothesis) and the alternative hypothesis would be the complement different from 1.7. And the best system of hypothesis are:

Null hypothesis:
`\mu =1.7`

Alternative hypothesis

Alternative hypothesis [tex]\mu \\eq 1.7[/tx]

And the best system of hypothesis are:

3. This two-sided test:

H0: μ = 1.7 mm

H1: μ ≠ 1.7 mm