Question

A sample of 10 bushings were taken from a shipment of 250 bushings and their outside diameters were measured. The following data are obtained:

Sample Number	Length (inches)
1	0.499
2	0.499
3	0.500
4	0.502
5	0.501
6	0.502
7	0.502
8	0.498
9	0.501
10	0.499

1. A manufacturing turning process was designed to achieve a targeted outside diameter of .502 for a shaft. Recent assembly problems have occurred where the shafts are too loose. As the QE investigating the issue, you decide to pull a sample of 10 shafts from inventory, measure the OD, and determine statistically if the shafts are lower on the average than the target of .502. What hypothesis should you formulate?

Descriptive Statistics: Length

1. H_o: μ _{shaft OD} ≥ .502     H₁: μ _{shaft OD} < .502   
2. H_o: μ _{shaft OD} = .502     H₁: μ _{shaft OD} ≠ .502    
3. H_o: μ _{shaft OD} ≤ .502     H₁: μ _{shaft OD} >.502   

1. Is this a one tail or two tail test?    ______________________________________

2. What or the degrees of freedom equal to? _____________________________

3. What type of test should you perform? ________________________________

4. What did you conclude relative your hypothesis and why?  

Answer 1

Solution:-

(c) State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u < 0.502
Alternative hypothesis: u > 0.502

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.0004726
DF = n - 1

D.F = 9
t = (x - u) / SE

t = -3.597

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of -3.597.

Thus the P-value in this analysis is less than 0.003

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that the shafts are higher on the average than the target of 0.502.