[This exercise requires a computer program to carry out the analysis of variance compu tations. An experiment was carried out to test the effects on yields of five varieties of corn and five types of fertilizer. For each variety-fertilizer combination, six plots were used and the yields recorded, with the results shown in the table.

(a) Test the null hypothesis that the population mean yields are the same for all five vari- eties of corn.

(b) Test the null hypothesis that the population mean yields are the same for all five brands of fertilizer.

(c) Test the null hypothesis of no interaction between variety and fertilizer.

1. The production process for an electronic component has been monitored. and the strength of electrical emission of the components has been measured. Results are available for a se- quence of thirty samples, each of seven observations. The overall mean of the sample ob- servations was 192.6, and the average sample standard deviation was 5.42.

(a) Use an unbiased estimator to find un estimate of the process standard deviation.

(b) Find the central line and lower and upper control limits for an X-chart.

(c) Find the central line and lower and upper control limits for an x-chart. 2. Measures are taken on the resistance, in ohms, of an electrical component. A sequence of twenty-five samples, each of six observations, was drawn. The overall mean of the sample observations was 93.2 and the average sample standard deviation was 3.67.

(a) Use an unbiased estimator to find an estimate of the process standard deviation.

(b) Find the central line and lower and upper control limits for an X-chart.

(c) Find the central line and lower and upper control limits for an x-chart.

3. Weights of samples of canned fruit were measured. A sequence of sixteen samples, each of eight observations, was taken. The overall mean of the sample observations was 19.86 ounces, and the average sample standard deviation was 1.23 ounces.

(a) Use an unbiased estimator to find an estimate of the process standard deviation.

(b) Find the central line and lower and upper control limits for an X-chart.

(c) Find the central line and lower and upper control limits for an s-chart. 4. Traditionally, in British quality control applications, control limits are set at 3.09 standard errors around the mean rather than three standard errors. Referring to Table 3 of the Appendix at the back of this book, explore the consequences and infer the rationale of this specification. 5. The accompanying table shows sample means and standard deviations for a sequence of thirty samples of eight observations each on a quality characteristic of a product.

(a) Find the overall mean of the sample observations.

(b) Find the average sample standard deviation.

(c) Use an unbiased estimator to find an estimate of the process standard deviation.

(d) Find the central line and lower and upper control limits for an X-chart.

(e) Draw the X-chart and discuss its features.

(f) Find the central line and lower and upper control limits for an s-chart. (g) Draw the s-chart and discuss its features. 6. The accompanying table shows sample means and standard deviations for a sequence of twenty samples of six observations each on contents weights of cans of vegetables, in ounces.

(a) Find the overall mean of the sample observations

(b) Find the average sample standard deviation.

(c) Use an unbiased estimator to find an estimate of the process standard deviation.

(d) Find the central line and lower and upper control limits for an X-chart.

(e) Draw the X-chart and discuss its features.

(f) Find the central line and lower and upper control limits for an s-chart. (g) Draw the s-chart and discuss its features.

7. Refer to Exercise 1. Management has specified that the strength of electrical emission of components produced by this process should be between 170 and 215.

(a) Compute the interval 30 and comment on your finding.

(b) Find the capability index. Cp. and discuss the result.

(c) Find the Cpk index and discuss the result. 8. Refer to Exercise 2. Management has specified that the resistance of components pro- duced by this process should be between 85 and 100 ohms.

(a) Compute the interval 30 and comment on your finding.

(b) Find the capability index. Cp. and discuss the result.

(c) Find the Cpk index and discuss the result. 9. Refer to Exercise 3. Management has specified that the weights of canned fruit should be between 18 and 22 ounces.

(a) Compute the interval 30 and comment on the result.

(b) Find and discuss the capability index Cp.

(c) Find and discuss the Cpk index.