DESCRIPTIVE STATISTICS

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 one(s)? What is the “SqFt” area of the outlier(s)? Is the outlier(s) smaller or larger than the average restaurant in the database? What can you conclude from this observation?

· What measure of central tendency is more appropriate to describe “Sales/SqFt”? Why?

The Java computer language, developed by Sun Microsystems, has the advantage that its programs can run on types of hardware ranging from mainframe computers all the way down to handheld computing devices or even smart phones. A test of 100 randomly selected programmers revealed that 71 preferred Java to their other most used computer languages. Construct a 95% confidence interval for the proportion of all programmers in the population from which the sample was selected who prefer Java.

Number of observations N=10 . Mean X= 22, Mean Y=15, Sum of squared deviations of X from mean value = 120, Sum of squared deviation of Y from mean value=144. Sum of multiplication of deviation of X and Y =124.From the above details the coefficient of correlation will be;

A manufacturing company produces plastic bottles for the dairy industry. Some of the bottles are rejected because of poor quality. Causes of poor-quality bottles include faulty plastic, incorrect labeling, discoloration, incorrect thickness, broken handle, and others. The following data for 500 plastic bottles that were rejected include the problems and the frequency of the problems. Use these data to construct a Pareto chart. Discuss the implications of the chart.

Two types of visits are provided by the Durham Health Clinic, first-time visits and return visits. Table 8-5 provides the processing time for each work station and the available staff hours per week. Determine the production frontiers for this clinic and indicate which station should be expanded to increase the overall capacity of the clinic. Which service station could be reduced?

Table 8-5 Processing Time and Staff Hours Data for Durham Health Clinic (Exercise 14-1)

· 8-2 Durham Health Clinic has a contribution margin of $35 per visit. Calculate the break-even point in visits with fixed costs at $4000, $6500, and $8500 per week. Given this analysis, as a manager, what would you recommend and why?

· 8-3 Durham Health Clinic is considering signing a contract to perform 50 pre-employment physicals per week for a specific corporation. In terms of staff time, a pre-employment physical requires 0.20 hours in Reception/Discharge, 0.45 hours in Nursing and Testing, and 0.20 hours in Medical Examination. By work-station, determine how many work hours per week will be needed to perform these physicals.

· 8-4 Currently the clinic does 250 visits per week, with 50% of all visits as return visits. Each employee (physician, nurse, and receptionist) is scheduled to work 35 hours per week.

o a. How many employees by type does the clinic currently need?

o b. How many employees by type will the clinic need if it signs the contract for pre-employment physicals?

o c. If return visits shift to 10% of all regular visits, how many employees by type will the clinic need with and without the contract for pre-employment physicals?

o d. How will the answers to “b” and “c” change if the number of physicals is modified to 35 pre-employment physicals per week?

Throughout these analyses, specify all assumptions, including assumptions concerning worker productivity.

· 8-5 How would your answers change for problem 8-1 if nursing and testing time was increased to 0.50 hours for both first and repeat visits, and medical exam and treatment time was reduced to 0.30 hours for a first visit and 0.20 hours for a return visit?

o Chapter 9: Exercises 9-1 and 9-2 (page 174 of the text)

EXERCISES

· 9-1 Alpha Walk-in Clinic operates as a single channel single server system. On Tuesdays, its average arrival rate (µ) per hour is 7.0. Analysis indicates that its service rate (?) is 8.5 patients per hour. Using queuing theory, describe this service system. What is:

o a. The probability that the clinic is idle—no patients waiting or being served?

o b. The average number of patients in the system?

o c. The average time (hours) a patient spends in the system (waiting + service time)?

o d. The average number of patients in the queue waiting for service?

o e. The average time (hours) a patient spends in the queue waiting?

o f. The probability that the patient, upon arrival, must wait?

· 9-2 The following data have been collected from a hospital pharmacy. This service system operates as a single server, single channel system.

· The service rate can be increased or decreased in increments of 50 prescriptions per hour. The expense associated with each 50-prescription increment is $100. In other words, to be able to process 50 additional prescriptions will cost an additional $100 per hour. If the current rate of processing or service is lowered by 50 prescriptions per hour, the savings are $100 per hour. Using queuing theory, describe this service system. What is:

o a. The probability that the clinic is idle—no patients waiting or being served?

o b. The average number of patients in the system?

o c. The average time (hours) a patient spends in the system (waiting + service time)?

o d. The average number of patients in the queue waiting for service?

o e. The average time (hours) a patient spends in the queue waiting?

o f. The probability that a patient, upon arrival, must wait?

Given the associated costs, should the service rate be changed? What are the financial implications associated with your recommendations?

How would you explain the meaning of the standard deviation or dispersion in the results?

When you analyzed these two variables together to determine the hours watching TV by marital status, what do you find from the data? What would be the research question?

Dr. Long

The following questions are from the ADHD Treatment (AT) case study.

This study investigated the cognitive effects of stimulant medication in children with mental retardation and Attention-Deficit/Hyperactivity Disorder. This case study shows the data for the Delay of Gratification (DOG) task. Children were given various dosages of a drug, methylphenidate (MPH) and then completed this task as part of a larger battery of tests. The order of doses was counterbalanced so that each dose appeared equally often in each position. For example, six children received the lowest dose first, six received it second, etc. The children were on each dose one week before testing.

This task, adapted from the preschool delay task of the Gordon Diagnostic System (Gordon, 1983), measures the ability to suppress or delay impulsive behavioral responses. Children were told that a star would appear on the computer screen if they waited “long enough” to press a response key. If a child responded sooner in less than four seconds after their previous response, they did not earn a star, and the 4-second counter restarted. The DOG differentiates children with and without ADHD of normal intelligence (e.g., Mayes et al., 2001), and is sensitive to MPH treatment in these children (Hall & Kataria, 1992).

1. (AT#1) What is the independent variable of this experiment? How many levels does it have?

2. (AT#2) What is the dependent variable? On what scale (nominal, ordinal, interval, ratio) was it measured?

Age For the following questions, use only the “age” column: Frequency Distribution: Class Width, Class Limits ,Relative Frequency ,Cumulative Relative Freg Midpoint, Mean *Round to two decimals Median *Round to one decimal Sample Standard deviation: *Round to two decimals Q1 * Round to one decimal Q3 * Round to one decimal DRAW :- 1) Ogive CURV : Polygon

A study investigated the condition of two different arteries, harvested from 110 candidates for coronary artery bypass surgery: the radial artery (RA) from the arm, and the internal thoracic artery (ITA) from the chest. In this question, you will look at the outcome “medial calcification of the radial artery” (yes/no), and patient factors which may affect this outcome. It is an important outcome, because radial arteries with medial calcification may not be suitable for use in bypass surgery.

The data is in the filegraft_arteries.csv on the LMS. Read the data into R. The name of the outcome (or response variable) has been shortened toRAcalc.

(a) We will consider two explanatory variables – presence or absence of diabetes, and presence or absence of hypertension. Usingtable(), create a table of the frequencies of the 8 combinations of the response variable and the two explanatory variables.

Using these frequencies, create a data frame suitable for logistic regression. The first of the 4 rows of this data frame should look something like this:

Diabetes Hypertension RAcalc total

no no 4 41