Question

For the following question complete the following:

1. State the null and alternative hypothesis

2. Determins the distribution to be used, and state the level of significance.

3. Calculate the Test Statistic

4. Draw a conclusion by comparing the p value to the level of significance and interpret the decision.

A manufacturer must test that his bolts are 2.00 cm long when they come off the assembly line. He must recalibrate his machine if the bolts are either too long or too short. After sampling 100 randomly selected bolts off the assembly line, he calculates the sample mean to be1.90 cm. He knows that the population standard deviation is 0.05cm. Assuming a level of significance of 0.05, is there significant evidence to show that the manufacture needs to recalibrate the machine?

Answer 1

Claim : To test whether that the manufacture needs to recalibrate the machine or not

Hypothesis :

Two tailed test

Note that the population Standard deviation is known to us.

i.e. Population SD =

Therefor , Z test appropriate to use for testing the hypothesis.

Test statistics :

Where, sample mean =

Sample SD

Sample size = n = 100

we get , test statitic = z = -20

Pvalue : By using the excel we get exact pvalue

Excel command is =NORMSDIST(z)

=NORMSDIST(-20)

= 0.000   

Pvalue = 0.000

Pvalue = 0

Decision Rule : We Reject Ho

Conclusion : There is sufficient evidence to conclude that that the manufacture needs to recalibrate the machine.