Question

Question #6

Beth’s Ltd manufactures screws which are used to manufacture tables. The table manufacturers, M & M Ltd, require that the screws have a length of 150 mm, with a small tolerance for differences in length. Beth’s Ltd randomly sampled and measured the average length of screws for 25 production runs. Due to the fact that the table manufacturers require a small tolerance for differences in the length of the screws, a 5% (0.05) significance level for evaluation was chosen. After measuring the average of the samples and their standard deviation, it was observed that the sample values were normally distributed about the mean.

Assume Beth’s Ltd derived the following values from their test and hypothesis:

Mean = 150.12
Standard Deviation = 0.496

Beth’s hypothesis:

H₀: The widget sizes equal 150
H_A: The widget sizes do not equal 150.

Requirements:

Consider the above scenario, and conduct a hypothesis test using the 95% confident level with a .05 significance level. In your answer, include the different steps to conduct a hypothesis test, see below.

•Null and alternative hypotheses

•Level of significance  

•Test statistics

•Rejection region and critical values

•Process of checking to see whether the test statistic falls in the rejection region

•Conclusion in words

                                   

Answer 1

Step 1:

H0:Null Hypothesis: = 150 ( The widget sizes equal 150 ) (Claim)

HA: Alternative Hypothesis: 150 ( The widget sizes do notequal 150 )

Step 2:

Level of significance = = 0.05

Step 3:

n = 25

= 150.12

s = 0.496

Test Statistic is given by:

Step 4:

=0.05

df = 25 - 1 = 24

From Table, critical values of t = 2.064

Rejection Region:
Reject H0 if t < - 2.064 OR t > 2.064

Step 5:

Since the test statistic = 1.24 does not fall in the rejection region, the difference is not significant. Fail to reject null hypothesis.

Step 6:
Conclusion:

The data support the claim that the widget sizes equal 150 .