Business Statistics for

Decision Makers

Analytics – Our ScopeSession Topic (including subtopics) Book Ref

1

Introduction to Statistics:

Origin of statistics

Functions and scope of statistics

The D-COVA lifecycle

The pyramid of statistics

Data Variables

Data and variables

Measurement scales

1

2

Data Visualization

Basic statistical visualization tools – pareto diagram,

histogram, ogive/cumulative frequency polygon, scatterplot

2

3

Descriptive Statistics

Measures of central tendency

Measures of variability/ dispersion

Measures of asymmetry/shape

Quartiles, 5-number summary and outliers

3

4

Probability Data Distribution

Basic concepts of probability

Discrete and Continuous distributions

Binomial Distribution

Excel functions binomial distribution

Poisson Distribution (If time permit)

4 and 5

5

Probability Data Distribution

Normal Distribution

Excel functions for normal distribution and their applications

6

Session Topic (including subtopics) Book Ref

6

Sampling Distribution

Concept and importance of inferential statistics

Central limit theorem

Sampling Distribution Numerical

7

7

Confidence Interval (CI) Estimation

Estimating confidence interval (CI) for the population mean

Estimating confidence interval for the population proportion

8

Hypothesis Formulation

Concept and importance of null and alternative hypothesis

Hypothesis formulation

Type 1 and Type 2 error

9

8

Hypothesis Testing

Applications of critical value hypothesis testing approach

Applications of p-value hypothesis testing approach

9

Correlation and Covariance

Association and causation

Correlation coefficient and covariance

13

9

Regression Analysis

Introduction to Simple and multiple linear Regression

Analysis

Equation of the Regression Line

Goodness of fit of the model

Coefficient of Determination R2

Implementing Regression in MS Excel

14, 15

10

Recap

Q&A

Practice caselets and exercises on key statistical techniques

Not

Applicable

Practice Session

a. 25

b. 25

c. 20

d. 20

e. 35

f. 128.571

g. 11.339

A small town has 5,600 residents. The residents in the town were asked whether or not they favored building a new bridge across the river. You are given the following information on the residents' responses, broken down by sex.

Men Women Total

In Favor 1,400 280 1,680

Opposed 840 3,080 3,920

Total 2,240 3,360 5,600

Let: M be the event a resident is a man

W be the event a resident is a woman

F be the event a resident is in favor

P be the event a resident is opposed

a. Find the joint probability table.

b. Find the marginal probabilities.

c. What is the probability that a randomly selected resident is a man and is in favor of building

the bridge?

d. What is the probability that a randomly selected resident is a man?

e. What is the probability that a randomly selected resident is in favor of building the bridge?

f. What is the probability that a randomly selected resident is a man or in favor of building the

bridge?

g. A randomly selected resident turns out to be male. Compute the probability that he is in

favor of building the bridge.

A Company supplies pins in bulk to a customer. The company uses an automatic lathe to produce the pins. Dueto many causes - vibrations, temperature, wear and tear, and the like - the lengths of the pins made by themachine are normally distributed with a mean of 1.012 inches and a standard deviation of 0.018 inch. Thecustomer will buy only those pins with lengths in the interval 1.00 0.02 inch. In other words, the customerwants the length to be 1.00 inch but will accept up to 0.02 inch deviation on either side. This 0.02 inch is knownas tolerance.

1) What percentage of the pins will be acceptable to the customer? (Ans: 63.39 %)

In order to improve percentage accepted, the production manager and the engineers discuss adjusting thepopulation mean and standard deviation of the length of the pins.

2) If the lathe can be adjusted to have the mean of the lengths to any desired value, what should it be adjustedto? Why? (Ans: Mean = 1.00, As it will help to increase the acceptance to 73.35 %)

3) Suppose the mean cannot be adjusted, but the standard deviation can be reduced. What maximum value ofthe standard deviation would make 90% of the parts acceptable to the consumer? (Assume the mean to be1.012.) (Ans: 0.006243)

4) Repeat question 3, with 95% and 99% of the pins acceptable. For 95% - 0.0048686; For 99% 0.003443858)

A Company supplies pins in bulk to a customer. The company uses an automatic lathe to produce the pins. Dueto many causes - vibrations, temperature, wear and tear, and the like - the lengths of the pins made by themachine are normally distributed with a mean of 1.012 inches and a standard deviation of 0.018 inch. Thecustomer will buy only those pins with lengths in the interval 1.00 0.02 inch. In other words, the customerwants the length to be 1.00 inch but will accept up to 0.02 inch deviation on either side. This 0.02 inch is knownas tolerance.

1) What percentage of the pins will be acceptable to the customer? (Ans: 63.39 %)

In order to improve percentage accepted, the production manager and the engineers discuss adjusting thepopulation mean and standard deviation of the length of the pins.

2) If the lathe can be adjusted to have the mean of the lengths to any desired value, what should it be adjustedto? Why? (Ans: Mean = 1.00, As it will help to increase the acceptance to 73.35 %)

3) Suppose the mean cannot be adjusted, but the standard deviation can be reduced. What maximum value ofthe standard deviation would make 90% of the parts acceptable to the consumer? (Assume the mean to be1.012.) (Ans: 0.006243)

4) Repeat question 3, with 95% and 99% of the pins acceptable. (Ans: For 95% - 0.0048686; For 99%0.003443858)

a) 19; approximately 50% of the

students work at least 19 hours

b) 26; at least 70% of the students work

less than or equal to 26 hours per week

c) 40; the most frequent data element

Average of X = 25; Average of Y = 200; and r = 0.0227

The value for b0 will be around

95 145 195 245 295

X 10 10 11 25 25 39 40 40

Y 100 200 300 100 300 100 200 300

Average of X = 25; Average of Y = 2000; and b0 = -979

The value for r will be

a) Positiveb) Negativec) Near to Zerod) None of thesee) Cannot be determined

Thank You!

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