Question

For each situation, state the null and alternative hypotheses: (Type "mu" for the symbol μμ , e.g. mu >> 1 for the mean is greater than 1, mu << 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1. Please do not include units such as "mm" or "$" in your answer.)

(a) The diameter of a spindle in a small motor is supposed to be 3.7 millimeters (mm) with a standard deviation of 0.12 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 3.62 mm

Answer 1

The diameter of a spindle in a small motor is supposed to be 3.7 millimeters (mm) with a standard deviation of 0.12 mm. If the spindle is either too small or too large, the motor will not work properly

So here we want that mean of diameter of a spindle in a small motor is not below or above value.

So it is two sided test.

Here we want go to test that the mean diameter of a spindle in a small motor is equal to or not 3.7 mm

mu:- population mean diameter of spindle in a small motor in mm

Ho:- mu = 3.7

Vs

Ha:- mu not = 3.7