Question

the diameter of a spindle in a small motor is supposed to be 5.9 millimeters (mm) with a standard deviation of 0.2 mm. if the spindle is either too small or too large, the motor will not work properly. the manufacturer measures the diameter in a sample of 15 spindles to determine whether the mean diameter has moved away from the required measurement. suppose the sample has an average diameter of 5.84 mm.

Answer 1

The correct set of null and alternative hypotheses for this scenario would be: A. H0: Mean = 5 and Ha: Mean is not equal to 5

In hypothesis testing, the null hypothesis (H0) typically represents the status quo or a claim that there is no effect, while the alternative hypothesis (Ha) represents the claim that is being tested. In this case, the manufacturer is testing whether the mean diameter has moved away from the target of 5 mm. The null and alternative hypotheses can be formulated as follows:

`\[ H_0: \text{Mean} = 5 \]\[ H_a: \text{Mean is not equal to 5} \]`

This corresponds to option A:

`\[ A. \quad H_0: \text{Mean} = 5 \quad \text{and} \quad H_a: \text{Mean is not equal to 5} \]`

This means the manufacturer is testing whether the mean diameter is different from 5 mm, indicating a two-tailed test where they are interested in any significant deviation from the target value.

The complete question is:

The diameter of a spindle in a small motor is supposed to be 5 mm. If the spindle is either too small or too large, the motor will not work properly. The manufacturer measures the diameter in a sample of motors to determine whether the mean diameter has moved away from the target. What are the null and alternative hypotheses (H0 = null hypothesis and Ha = alternative hypothesis)?

A.H0: Mean= 5 and Ha: Mean is not equal to 5

B.H0: Mean = 5 and Ha: Mean <5

C.H0: Mean < 5 and Ha: Mean > 5

D.H0: Mean = 5 and Ha: Mean > 5