Question

The mean 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 perform properly. The manufacturer measures the diameter in a sample of 60 motors to determine whether the mean diameter has moved away from the target. They found the mean diameter of the sample to be 4.951 mm. From past studies it is known that the population standard deviation is 0.2 mm. Write Ho. Hgand use Hypothesis testing to test the cairm that the diameter of a spindle in a small motor is different from 5 mm is supported or not supported based on a = 0,1, 0.05 and 0,01.

Answer 1

Solution:

The null and alternative hypotheses are:

Under the null hypothesis, the test statistic is:

The p-value is:

Now using the standard normal table, we have:

Conclusion: Since the p-value is less than the significance level 0.1, we, therefore, reject the null hypothesis and conclude that the mean diameter of a spindle in a small motor is different from 5 mm at the 0.1 significance level.

But the p-value is greater than the significance level's 0.05 and 0.01, we, therefore, fail to reject the null hypothesis and conclude that the mean diameter of a spindle in a small motor is not different from 5 mm at the 0.05 and 0.01 significance levels.