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

In hypothesis testing procedure the trait of null hypothesis is that it always contain an equality sign. We are known that diameter of spindle is known to be 5mm. This our null value. Hence the null hypothesis is

H0:μ=5.

Now for alternative hypothesis we are given that the mean diameter has moved away from the target. This means that mean diameter could be increases or decreases from 5mm. Hence the alternative hypothesis is

Ha:μ≠5

joaobezerra joaobezerra · Answer 2 · 2021-11-18T12:06:23+01:00

From the information given, it is found that the correct option is:

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

At the null hypothesis, it is tested if the motor works properly, that is, the spindle has diameter significantly close to 5 mm, hence:

[tex]H_0: \mu = 5[/tex]

At the alternative hypothesis, it is tested if the motor does not work properly, that is, the spindle has diameter different from 5 mm, either too high or too low, hence:

[tex]H_a: \mu \neq 5[/tex]

Thus, a is the correct option.

A similar problem is given at https://brainly.com/question/15704285