Category Archives: Statistics

Calculate the mean, standard deviation, skew, 5-number summary, and interquartile range (IQR) for each of the variables.

In preparation for writing your report to senior management next week, conductthe following descriptive statistics analyses with Excel®. Answer the questions below in your Excel sheet or in a separate Word document:

· Insert a new column in the database that corresponds to “Annual Sales.” Annual Sales is the result of multiplying a restaurant’s “SqFt.” by “Sales/SqFt.”

· Calculate the mean, standard deviation, skew, 5-number summary, and interquartile range (IQR) for each of the variables.

· Create a box-plot for the “Annual Sales” variable. Does it look symmetric? Would you prefer the IQR instead of the standard deviation to describe this variable’s dispersion? Why?

· Create a histogram for the “Sales/SqFt” variable. Is the distribution symmetric? If not, what is the skew? Are there any outliers? If so, which….

Run the two-way analysis of variance. Give the results of the hypothesis tests for the main effects and the interaction.

Refer to Exercise 13.43. Additional data collected by the same researchers according to a similar design are given in the PLANTS2 data file. Here, there are two response variables. They are fresh biomass and dry biomass. High values for both of these variables are desirable. The same four species and seven levels of water are used for this experiment. Here, however, there are four plants per species-by-water combination. Analyze each of the response variables in the PLANTS2 data file using the outline from

Exercise 13.43

The PLANTS1 data file gives the percent of nitrogen in four different species of plants grown in a laboratory. The species are Leucaena leucocephala, Acacia saligna, Prosopis juliflora, and Eucalyptus citriodora. The researchers who collected these data were interested in commercially growing these….

Run a separate oneway analysis of variance for each species and summarize the results. Since the amount of water is a quantitative factor, we can also analyze these data using regression.

Perform the tasks described in Exercise 13.46 for the two response variables in the PLANTS2 data file

Exercise 13.46

Refer to Exercise 13.43. Run a separate oneway analysis of variance for each species and summarize the results. Since the amount of water is a quantitative factor, we can also analyze these data using regression. Run simple linear regressions separately for each species to predict nitrogen percent from water. Use plots to determine whether or not a line is a good way to approximate this relationship. Summarize the regression results and compare them with the one-way ANOVA results.

Exercise 13.43

The PLANTS1 data file gives the percent of nitrogen in four different species of plants grown in a laboratory. The species are Leucaena leucocephala, Acacia saligna, Prosopis juliflora, and….

Make a flowchart of this process, making sure to include steps that involve Yes/No decisions

Refer to the previous exercise. The time it takes from deciding to order a sandwich to receiving the sandwich will vary. List several common causes of variation in this time. Then list several special causes that might result in unusual variation

Previous exercise

Consider the process of calling in a sandwich order for delivery to your apartment. Make a flowchart of this process, making sure to include steps that involve Yes/No decisions

What type of control chart will you use?

At the present time, about 5 out of every 1000 lots of material arriving at a plant site from outside vendors are rejected because they do not meet specifications. The plant receives about 350 lots per week. As part of an effort to reduce errors in the system of placing and filling orders, you will monitor the proportion of rejected lots each week. What type of control chart will you use? What are the initial center line and control limits?

find the appropriate center line and control limits for an x¯ chart, make the x¯ chart, and comment on control.

Interviews with the operators reveal that in Samples 1 and 10 mistakes in operating the interferometer resulted in one high-outlier thickness reading that was clearly incorrect. Recalculate x¯ and s after removing Samples 1 and 10. Recalculate UCL for the s chart and add the new UCL to your s chart from the previous exercise. Control for the remaining samples is excellent. Now find the appropriate center line and control limits for an x¯ chart, make the x¯ chart, and comment on control.

What is the estimate σ^ of the process standard deviation based on the sample standard deviations (after removing Samples 1 and 10)?

The specifications call for film thickness 830 ± 25 mm × 10−4.

(a) What is the estimate σ^ of the process standard deviation based on the sample standard deviations (after removing Samples 1 and 10)? Estimate the capability ratio Cp and comment on what it says about this process.

(b) Because the process mean can easily be adjusted, Cp is more informative than Cpk. Explain why this is true.

(c) The estimate of Cp from part (a) is probably too optimistic as a description of the film produced. Explain why

What type of control chart would be used in this setting, and what would be the control limits for a sample of 100 films?

Previously, control of the process was based on categorizing the thickness of each film inspected as satisfactory or not. Steady improvement in process quality has occurred, so that just 15 of the last 5000 films inspected were unsatisfactory.

(a) What type of control chart would be used in this setting, and what would be the control limits for a sample of 100 films?

(b) The chart in part (a) is of little practical value at current quality levels. Explain why.