# Statistical Analysis of Defective Items

1. A production manager is interested in determining the variability in the proportion of defective items in a shipment in one of the computer components that her company manufactures. The spreadsheet provided contains the proportion of defective components for each of the 500 randomly selected shipments collected during the one month period. Compute the sample standard deviation of these data. Discuss whether empirical rules apply.

(As part of this problem, construct a Frequency Table and Histogram of the Defective Items Proportions. Use the Standard Deviation as the bin size. Now it is a simple matter to compare the expected frequencies (based on the Empirical Rules) with the observed frequencies in the data. The Histogram provides a visual clue as to whether the Empirical Rules are followed. You do not need to change the data at all here. It is ok to make comparisons of proportions.)

2. Data on the numbers of the insured commercial banks in the United States are given on the spreadsheet provided.

a. Compare these distributions of the numbers of the US commercial banks (one for each year). Are the mean and standard deviation of these numbers changing over time? If so, how do you explain the trends?

b. What trends do you notice in the numbers of commercial banks by region? For example, how do the numbers of commercial banks appear to be changing in the northeastern United States over the given period? Summarize your findings for each region of the country.

(For Part 1, create a table and a graph of the MEAN and STDEV by year. If you look at the file provided with the textbook, pay careful attention to how the summaries ("Northeast," "Midwest," ...) are created in order to avoid "double counting" the data. For Part 2, construct a Pivot Table and a Pivot Chart to illustrate the answer to the question.)

3. The ACCRA Cost of living index provides useful and reasonably accurate measure of cost of living differences among a large number of urban areas. Items on which the index is based have been carefully chosen to reflect the categories of consumer expenditures. The spreadsheet is provided and is labeled problem 14 chapter 11. Use the data given to estimate t he simple linear regression models to explore the relationship between the composite index (i.e. independent variable) and each of the various expenditure components (i.e. explanatory variable).

a. Which expenditure component has the strongest linear relationship with the composite index?

b. Which expenditure component has the weakest linear relationship with the composite index

(Create a separate linear regression for each independent variable. In this case the Composite_Index is the dependent variable. How do you compare the "strength" of relationships using linear regression? )

Question: How does one interpret the relationship between two numeric variables when the estimated least squares regression line for them is essentially horizontal (i.e. flat)

#### Solution Summary

This solution is comprised of detailed step-by-step calculations and analysis of the given problems related to Statistics and provides students with a clear perspective of the underlying concepts.