A company produces an item that is supposed to have a six centimetre hole punched in the centre.A quality control inspector is concerned that the machine which punches the hole is "out-of-control" (hole is too large or too small).In an effort to test this, the inspector is going to gather a sample punched by the machine and measure the diameter of the hole.The alternative hypothesis used to statistical test to determine if the machine is out-of-control is A)the mean diameter is 6 centimetres. B)the mean diameter is

Question

A company produces an item that is supposed to have a six centimetre hole punched in the centre.A quality control inspector is concerned that the machine which punches the hole is "out-of-control" (hole is too large or too small).In an effort to test this, the inspector is going to gather a sample punched by the machine and measure the diameter of the hole.The alternative hypothesis used to statistical test to determine if the machine is out-of-control is
A)the mean diameter is > 6 centimetres.
B)the mean diameter is < 6 centimetres.
C)the mean diameter is = 6 centimetres.
D)the mean diameter is ≠ 6 centimetres.
E)the mean diameter is ≥ 6 centimetres.

Quizplus · Accepted Answer

The alternative hypothesis in this case should be that the mean diameter is not equal to 6 centimetres, since we want to test if the machine is producing holes that are either too large or too small. A two-tailed test is appropriate since we are looking for deviations in either direction from the hypothesized value. Therefore, the best choice is D, which states that the mean diameter is not equal to 6 centimetres.

A Company Produces an Item That Is Supposed to Have