Two new vendors are being considered to supply a critical part for assembly into a new product. Both vendors provided a sample of the parts for evaluation. You are the quality engineer assigned to evaluate the product and make a recommendation for the vendor to be chosen. Part 1. Evaluation of Vendor A A random sample of 16 parts, submitted by Vendor A for evaluation, yielded the following measurements: 2.13 2.15 2.16 2.18 2.15 2.18 2.16 2.13 2.16 2.16 2.14 2.15 2.13 2.17 2.12 2.17 =2.1525 s=0.01844 a) Based on the sample data, what is the 95% confidence interval for the population mean? b) The vendor claimed that the mean of his process is 2.1. With 95% confidence, can you reject the null hypothesis that the true mean is 2.1? (Two tailed test. Use comparison to tcritical -note the p value when you check with Minitab.) P value (from Minitab)= ______________ c) If the specifications for the part are 2.1 0.15, what would you estimate the process capability ratios of Cp and Cpk to be? (We cannot verify the process is stable, but we can get an estimate the capability using the mean and standard deviation from the sample.) Do you consider the vendor capable? Part 2. Evaluation of Vendor B

A second vendor, B, is also being evaluated. 12 parts are submitted for evaluation. The measurements on these parts are as follows: 2.09 2.13 2.17 2.13 2.08 2.18 2.12 2.10 2.12 2.13 2.17 2.07 = 2.1242 s=0.03580 d) Based on the sample data, what is the 95% confidence interval for the population mean? e) The vendor claimed that the mean of his process is 2.1. With 95% confidence, can you reject the null hypothesis that the true mean is 2.1? (Two tailed test. Use comparison to tcritical -note the p value when you check with Minitab.) P value (from Minitab)= ______________

f) If the specifications for the part are 2.1 0.15, what would you estimate the process capability ratios of Cp and Cpk to be for this vendor? Part 3. Comparison of vendors g) Perform a two sample hypothesis tests of the variances. With 95% confidence can you conclude that the variance of vendor A is lower than vendor B? (Use comparison to Fcritical. Note the p value when checking with Minitab.) P value (from Minitab)= ______________ Based on this test, when performing an hypothesis test on the means for these vendors, which of these assumptions should be used? (check one) _____ Assume variances not equal. (d.f. = 15) ____ Assume equal variances (sp=.0272) h) Perform the appropriate two sample hypothesis test of the means to assess if vendor A has a larger mean than vendor B with 95% confidence. (Use comparison to tcritical -note the p value when you check with Minitab.) P value (from Minitab) = __________

Part 5. Summary and conclusions Complete the following table:

	Vendor A	Vendor B
Sample mean
Sample standard deviation
Confidence interval for mean
Cp
Cpk
P value(from Minitab output) for difference of the means, and hypothesis test conclusion
P value (from Minitab output)for the difference of the variances and hypothesis test conclusion

Which vendor was closer, on average, to the target value of the specification? Which vendor had a lower standard deviation? Compare Cp and Cpk for the two vendors. How do these relate compared to their closeness of the means to the target and their standard deviations? Based on the above data, which vendor would you select? Why? Questions

Question 1

In part 1a, the t value used to determine the confidence interval is

Group of answer choices

2.120

2.131

1.753

1.756

Question 2

In part 1b, the conclusion of the test is

Group of answer choices

The p value is very low so the null hypothesis that the sample came from a population where the mean is 2.1 cannot be rejected.

The vendor's sample mean is too low to be from a population where the mean of the population is 2.1.

None of other responses are correct.

The vendor claim of having a mean of 2.1 is not supported.

Question 3

From the determination of C_p and C_pk in part 1c, it can be determined for vendor A that

Group of answer choices

The process must be centered to be capable.

The process is capable but shifted towards the upper specification.

The process is not capable even if centered.

The process is skewed towards the lower specification.

Question 4

In part 2d, in determining the 95% confidence interval for the population mean for vendor B, which of the following is not true?

Group of answer choices

The interval is [2.1014,2.1469]

None of the above. (All of the above are true.)

The t value to be used is 2.201.

The degrees of freedom is 12.

Question 5

In part 2e, if the level of confidence required is 95%, the conclusion of the test is

Group of answer choices

The null hypothesis that the mean of the process is 2.1 cannot be rejected.

The null hypothesis that the mean of the sample is 2.1209 cannot be rejected.

It is not plausible that the mean of the process producing vendor B parts is 2.1.

The alternative hypothesis that the mean of the process is not equal to 2.1209 is accepted.

Question 6

In part 2e, the smallest level of risk, alpha, which would cause rejection of the null hypothesis is

Group of answer choices

0.026

0.039

0.052

0.012

Question 7

In Part 2f, Cpk for vendor B is determined to be

Group of answer choices

1.40

Equal to Cpu

0.95

Equal to Cpl

Question 8

In part 3g, the Ftest statistic is

Group of answer choices

1.946

2.510

The variance of vendor A divided by the variance of vendor B

The variance of vendor B divided by the variance of vendor A.

Question 9

In part 3h, from the hypothesis test, which of the following is notcorrect?

Group of answer choices

None of the above. (All of the above. are true statements.)

The value of tcritical is 1.753.

The statistical conclusion is that the null hypothesis is rejected as |t_test|>t_critical

The null hypothesis of the test is that the mean of Vendor A's process is equal to the mean of vendor B's process.

Question 10

In part 5, which statement is true regarding comparison of the capability data for the two vendors?

Group of answer choices

Although Vendor B has higher capability than Vendor A, Vendor A would be preferred to vendor because it is on average closer to target.

All of the above.

If both Vendor A and B centered their processes, Vendor A would have an even higher capability than vendor B

The reason that Vendor B has higher capability ratios than A is because it has higher variability in the process.