Question

The diameter of a spindle in a small motor is supposed to be 5.8 millimeters (mm) with a standard deviation of 0.14 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 12 spindles to determine whether the mean diameter has moved away from the required measurement. Suppose the sample has an average diameter of 5.88 mm. 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.

Answer 1

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

Step-by-step explanation:

Definitions:

• Null hypothesis $(H_0)$ is a statement describing population parameters according to the objective of the study. It takes "≤,≥,=" signs.  
• Alternative hypothesis$(H_a)$  is a statement opposite to the null hypothesis elaborating population parameters according to the objective of the study. It takes ">, <, ≠" signs.

Given: The diameter of a spindle in a small motor is supposed to be 5.8 millimeters.

If the spindle is either too small or too large, the motor will not work properly. so, Mean diameter ≠ 5.8 to work correctly.

i.e. $H_a: \text{Mean}\neq 5.8$

So, $H_a: \text{Mean =5.8}$

The required null and alternative hypotheses:

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