expert on excel using megastat

2

>Output B

inomial

distribution 6 n 0

.

5 p cumulative X P(X) probability

0 0.0

1

56

3 0.015

63 1

0.0

9

375 0.10938

2

0.23

4

38 0.3

43

75 3

0.3

12 50 0.65625 4

0.23438 0.89063 5 0.09375

0.98438 6

0.01563 1.0

0000 1.00000 3.0

00 expected value 1.500 variance 1.225 standard deviation 3.0
No

rmal distribution P(lower) P(upper)

z

X mean st

d.

dev .92

57 .0743 1.44 60,000 49

,400 7,340 2.0 Normal distribution P(lower) P(upper)

z

X mean

std.dev .

27

44 .7256 -0.60 45,000 49,400

7,340

Uniformly

D

istributed Random Numbers Minimum

1
Maximum 100 Uniform 70.84920

36

462

Uniformly Distributed Random Numbers
Minimum 1
Maximum 100

Uniform

53.80897

79

615 58

.37234

30

037 29.6666839123 30.8928530812 77.6992698908 2.3877465129 76.3116354942 81.6345

120

072 71.1947520971

Binomial distribution

(n = 6, p =

0.5

)

0.0 1.0 2.0 3.0

4.0 5.0 6.0

0.015625 0.09375 0.234375 0.3125 0.234375 0.09375 0.0156 25 X
P(X)

3
2
1
0

-1

-2

-3

f(z)

z
1.44

-1.28

3
2
1
0
-1
-2
-3
f(z)
z
-0.60

Sheet1

ounting Probability – combinations order does not count- in permutations order counts. This following shows how many combinations one permutations there are of 2 given 4 things.

A-B

B

A-C

C

A-D

D

B-C

B-D

C-D

6 12

1.0

ions, how many arrangements of new businesses locate there?

2.0

3.0

B

27

43 36 79

57 63 120

es shown here correspond to your experience? (d) Why might

ii. P(W) iii. P(S | W)

(S)

30 120

d.

4.0

24 50

No 49 58 100

Example
Binomial distribution

6 n

0.5 p

cumulative

X P(X) probability
0 0.01563 0.01563

1 0.09375 0.10938

2

3

0.65625
4 0.23438 0.89063
5 0.09375 0.98438
6 0.01563 1.00000
1.00000

expected value
1.500 variance
1.225 standard deviation

5.0

The mean annual income of workers in a particular industry is $49,400 with a standard deviation of $7340.

Normal distribution

P(lower) P(upper) z X mean std.dev

.0743 1.44 60,000 49,400 7,340

.0743

.9257 .0743 1.44 60,000 49,400 7,340

.7256 -0.60 45,000 49,400 7,340

6.0

one is research exactly. Then one must determine the appropriate sample size for the research. The sampling must be designed so everyone in the population as an equal chance of being selected (the procedures are Random, Cluster, Stratified, and Systematic – we will do an exercise using random selection)

Population

9

cat
Uniform Population Uniform Population

dog 2.3877465129 grizzly 1

cat 29.6666839123 bird 2

29.6666839123 bird 30.8928530812 lion 3
30.8928530812 lion 53.8089779615 dog 4
77.6992698908 elephant 58.3723430037 cat 5
2.3877465129 grizzly 71.1947520971 turtle
76.3116354942 polar bear 76.3116354942 polar bear

panda 77.6992698908 elephant

71.1947520971 turtle 81.6345120072 panda

grizzly
bird
lion

dog

cat

dog
cat
bird
lion
elephant
grizzly
polar bear
panda
turtle

rat
Example:

Week 3 – Probabilities
First we cover counting probabilities
	C
Things	Combinations	Permutations
A		A-B	B-A
	A-C	C-A
	A-D	D-A
	B-C	C-B
	B-D	D-B
	C-D	D-C
totals
If a new shopping center has seven lo					cat
Use Factorial to do.	use factorial
If seven business want to locate in a new shopping center but there are only five locations, how many
arrangements could there be?	use permutations
If seven bossiness want to locate in a new shopping center but there are only five locations, how many
different combinations could be selected?	use combinations
Discrete Probabilities: Concept and Binomial
Probability must between 0 and 1; total of all probabilities is 1
Concept is simply “The Specific Question” divided by the total possibilities (Excel for these)
	Example	Married	Not Married
-B
Sport car	14	41
Not sport car
Question: What is probability of being married = 57/120
Question: What is the probability of having a sports car and being married = 14/120
Question: What is the probability of having a spots car or being married =(41+57-14)/120
Another old example: Refer to the contingency table shown below. (a) Calculate each probability (i–vi) and explain in
words what it means. (b) Do you see evidence that smoking and race are not independent?
Explain. (c) Do the smoking	rat
public health officials be interested in this type of data? (Data are from Statistical Abstract of the
United States, 2001, pp. 12 and 16. Note: Actual statistics are applied to a hypothetical sample of
1,000.) Smoking2
i. P	(S)
iv. P(S | B) v. P(S and W) vi. P(N and B)
Smoking by Race for Males Age 18-	24
Smoker	Nonsmoker	Row Total
(N)
White (W)	290	560	850
Black (B)	150
Column Total	320	680	1000
a.-i	320/1000 =	probability of a smoker
a.-ii	850/1000=	probability of a White
a.iii	290/850=	probability of a While being a smoker
a.iv	30/150=	probability of a Black being a smoker
a.v	290/1000=	probability of selecting a White and being a smoker
a.vi	120/1000=	probability of selecting a Black and being a nonsmokeroer
b.	The P of smoking and white is .29 and the P(S)*P(W) =.32*.85=
The P of smoking and Black is .03 and the P(B)*P(S)=.32*.15 =
If smoking is dependent on race, then health officials might target special
programs based on race.
Your exercise to do
Size of company
Small	Medium	Large
Plan MBA?	Yes	105	179
207
73	108	205	386
P(Yes) =
P(Yes | Medium) =
P(Yes and Large) =
P(Small and Yes) =
P(Medium or Yes) =
P(Small) =
P(Medium | Yes) =
Now Binomial (MegaStat for these)
What is the probability of observing two heads is a coin is tossed six times?
n=6
P/head = .5
Use MegaStat to compute
Results
0.34375	Note the	Probability of throwing 2 heads is .23438
0.31250	3.000
Your turn:	A basketball team that shoots free throws at 80.5% shoots 14 free throws in their next game.
What is the Probability they will be successful in 11 of them?
and what is the probability they will be successful in at least 9 of them?
Now we do what is the very basis of much of statistics – six sigma -lean. The Normal Distribution
	Example:
Assume a normal distribution.
A. What is the probability a worker would have an income below $60,000?
Use MegaStat for this
	.9257
B. What is the probability a worker would have an income above $60,000?
C. What is the probability a worker would make between $45,000 and $60,000
.2744
0.6512
Your turn to do the exercise
Assume a college entrance exam has a mean of 1000 and a standard deviation of 100. Assume a normal distribution.
A. What is the probability the student’s score would be below 1000?
B. What is the probability the student’s score would be below 850?
C. What is the probability the student’s score would b above 1250″
D. What it the probability the student’s score would be between 850 and 1250?
E. What would be the student’s score to have only 5% of the students taking the test have higher >
Now sampling. Sampling is the basis of nearly all medical improvements and used in all industries
Sampling requires that one Identifies the			Population
Example – what is the required sample size for a customer with a .035 error and 95% confidence.
Answer:	784
7.0	Your turn:
A. Customer states he wants a 3% error with 95% confidence. What is the require sample size
B. What is the require sample size for a study have an error of 1,000 whose standard deviation is 7,800
and a 90% confidence level.
Now we randomly select
Example – random selection	Random select 5 from the following “population”.
				dog	N count of population =
				bird
				lion
			elephant
				grizzly
			polar bear
			panda
			turtle
Sort on Uniform
	53.8089779615
	58.3723430037
	81.6345120072
select top 5
8.0	Your turn.	Randomly select 7 from the following – show all your steps as in the example
mouse
squirrel
rabbit
skunk
And we end the week with confidence interval
A local retailer wants to know the 95% confidence interval of the proportion of customers who use a credit card. A
random sample of 142 receipts showed that 83 used a credit card.
95% confidence interval .503 to .666
9.0	Your Turn
A. Compute the 95% confidence interval of those people choosing chocolate ice cream. 12 of 27 customer
chose a favor other than chocolate.
B. Compute the 90% confidence interval when the mean is 12,000, the standard deviation is 500 and the N count is 86

&P of &N

Binomial distribution (n = 6, p = 0.5)
0.0 1.0 2.0 3.0 4.0 5.0 6.0 0.015625 0.09375 0.234375 0.3125 0.234375 0.09375 0.0156 25 X
P(X)

Sheet2

Sheet3