90%= 1.645 95% = 1.96 98% = 2.33 99% = 2.575 Hypothesis Testing
*A credit card company wondered whether giving frequent flyer miles for every purchase would increase card usage, which has a current mean of $2500 per year. They gave free flyer miles to a simple random sample of 25 card customers and found the sample mean to be $2542 and the standard deviation to be $109. n= 25 Ho (Claim) µ=2500 OR Ha µ > 2500 *Use t-table n .50 Ha a. 5% level of significance- Reject Ho, there is enough evidence to accept claim P ≤ .50 Hob. Error? Type I

N = 4000c. Right tailed
P = 2200/4000 d. CV = 1.645 Test Statistic= 6.325
z=p-ppqn
*A sample of 54 watercraft accidents reported to Nebraska revealed that 85% of them involved personal watercrafts. Suppose the national average of watercraft accidents is 78%. Does the accident rate in Nebraska exceed the rate in the nation? Use 0.01 level of significance. n=54 p≤ 0.78 Ho (Claim)

p=.85 p> 0.78 Ha
α=.01
z=p-ppqn Test Statistic= 1.24 CV= 2.33
Minimum Sample Sizes
*You wish to estimate, with 99% confidence , the proportion of computers that need repairs or have problems by the time the product is three years of. Your estimate must be accurate within 2% of the true proportion. Find the minimum sample size with no preliminary estimate. n=(Zc* σE)^2 n=pq(ZcE)^2 CV = 2.575 C = 99% *Confidence intervals are two tails!*

E= .02 *Must be rounded up with minimum sample size* p= .50 =4,145
Binomial
*When an assembly machine is properly calibrated approximately 5% are defective. Randomly selects 20 products. Production is halted if anything is defective. What is the probability the production must be halted? p(x)=(nCx)(px)(qn-x) n=20 x=0 p=.05 q=.95 Answer: 1-.95^20...

...Expectations, Variances & Covariances
The Rules of Summation
n
å xi ¼ x1 þ x2 þ Á Á Á þ xn
covðX; YÞ ¼ E½ðXÀE½XÞðYÀE½YÞ
i¼1
n
¼ å å ½x À EðXÞ½ y À EðYÞ f ðx; yÞ
å a ¼ na
x y
i¼1
n
covðX;YÞ
r ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
varðXÞvarðYÞ
n
å axi ¼ a å xi
i¼1
n
i¼1
n
n
i¼1
i¼1
E(c1X þ c2Y ) ¼ c1E(X ) þ c2E(Y )
E(X þ Y ) ¼ E(X ) þ E(Y )
å ðxi þ yi Þ ¼ å xi þ å yi
i¼1
n
n
n
i¼1
i¼1
å ðaxi þ byi Þ ¼ a å xi þ b å yi
i¼1
n
var(aX þ bY þ cZ ) ¼ a2var(X) þ b2var(Y ) þ c2var(Z )
þ 2abcov(X,Y ) þ 2accov(X,Z ) þ 2bccov(Y,Z )
n
å ða þ bxi Þ ¼ na þ b å xi
i¼1
If X, Y, and Z are independent, or uncorrelated, random
variables, then the covariance terms are zero and:
i¼1
n
å xi
x1 þ x2 þ Á Á Á þ xn
x ¼ i¼1n ¼
n
varðaX þ bY þ cZÞ ¼ a2 varðXÞ
n
å ðxi À xÞ ¼ 0
þ b2 varðYÞ þ c2 varðZÞ
i¼1
2
3
2
å å f ðxi ; yj Þ ¼ å ½ f ðxi ; y1 Þ þ f ðxi ; y2 Þ þ f ðxi ; y3 Þ
i¼1 j¼1
i¼1
¼ f ðx1 ; y1 Þ þ f ðx1 ; y2 Þ þ f ðx1 ; y3 Þ
þ f ðx2 ; y1 Þ þ f ðx2 ; y2 Þ þ f ðx2 ; y3 Þ
Expected Values & Variances
EðXÞ ¼ x1 f ðx1 Þ þ x2 f ðx2 Þ þ Á Á Á þ xn f ðxn Þ
n
¼ å xi f ðxi Þ ¼ å x f ðxÞ
x
i¼1
E½gðXÞ ¼ å gðxÞ f ðxÞ
x
E½g1 ðXÞ þ g2 ðXÞ ¼ å ½g1ðxÞ þ g2 ðxÞ f ðxÞ
x
¼ å g1ðxÞ f ðxÞ þ å g2 ðxÞ f ðxÞ
x
Normal Probabilities
XÀm
$ Nð0; 1Þ
s
2
If X $ N(m, s ) and a is a constant, then
a À m
PðX ! aÞ ¼ P Z !
s
If X $ Nðm; s2 Þ and a and b are constants; then
aÀm
bÀm
Z
Pða X bÞ ¼ P
s
s
If X $ N(m, s2), then Z ¼
Assumptions of the Simple Linear Regression
Model...

...Chapter 3
Standard units tell you how many standard deviations above or below average a data value is
standard units = (actual value – average)/SD
actual value = average + (SD x standard units). Standard units are denoted by Z.
Chapter 8
Complement rule: P(A) = 1 – P(A doesn't happen)
Multiplication rule:
P(A and B both happen) = P(A) x P(B given A happened)
Q. 5 random components removed one at a time from box containing 5 defective and twenty working. What is chance of selecting all defective:
A. 5/25x4/24x3/23x2/22x1/21. Selecting no defective 1 minus chance of selecting all defective or 20/25 x 19/24 x 18/23 x 17/22 x 16/21 = 2/7 or 29%
Q. Important data server breaks down 40% of the time, is operational the other 60%, and servers breakdown independently. How many independent servers should be running so that there is a 99% chance at least one is operational? (40%)^X = 1% (1% = chance none are operational)
A. .4^5 = .01024, so to get to .99 uptime, add another server.
Q. Consider two bonds with BB- ratings, chance of default 1.5%. What is the probability that both default within a year? A. .015 x .015 Q. What is the probability that neither defaults? A. .985 x .985 Q. What is the probability that exactly one defaults? A. P(exactly one) = 1 – P(neither) – P(both) = 1 - .015 x .015 - .985 x .985.
Independent: P(firm B defaults given A defaults) = P(firm B defaults) = .015
Dependant: P(firm A and B default) = P(firm A defaults) x P(firm B defaults given...

...A boy wants to play on the volleyball team but there are only all girl team. What amendment protects his rights?
The Fourteenth Amendment guarantees that "no state shall . . . deny to any person within its jurisdiction the equal protection of the laws." Added to the Constitution in 1868, this "equal protection clause" was aimed primarily at protecting the recently freed slaves against southern governments that had stripped the freedmen of their political and legal rights. The courts, however, have interpreted this clause, with its more inclusive reference to "any person," as providing a basic protection for all persons, not just African Americans.
As is evident from the foregoing analysis, the IGHSAU’s actions are to be considered “state actions” for purposes of applicability of the Fourteenth Amendment. Consequently, the rules and regulations of the IGHSAU are subject to the Equal Protection Clause of the Fourteenth Amendment.
Title IX prohibits sex discrimination under any educational program or activity that receives federal funds. 20 U.S.C. §1681(a). The Regulations define “recipient” as: Any State or political subdivision thereof, or any instrumentality of a State or political subdivision thereof, any public or private agency, institution or organization, or any other entity, or any person, to whom Federal financial assistance is extended directly or through another recipient and which operates education program or activity which receives or benefits from such...

...What proportion of a normal distribution is located in the tail beyond z = +2.00?
0.0228
What proportion of a normal distribution is located between the mean and z = 1.40?
0.4192
The Z-score corresponding to the 52nd percentile is
.05
A normally distributed variable has a mean of 10 and a standard deviation of 2. The probability that a value between 7 and 9 is obtained is
.2417
An accelerated life test on a large number of type-D alkaline batteries revealed that the mean life for a particular use before they failed is 19.0 hours. The distribution of the lives approximated a normal distribution. The standard deviation was 1.2 hours. About 95.44% of the batteries failed between what two values?
16.6 & 21.4
The average time students need to finish a particular test is 70 minutes with a standard deviation of 12 minutes. (Assume that these times are normally distributed.) If we want 90% of the students to have sufficient time to finish the test, how much time should we give them?
85.36 minutes
The distribution of sample means
will be normal if either the population is normal or if the sample size is greater than 30.
Increasing the alpha level (for example, from α=0.01 to α= 0.05)
Increases the probability of a Type I error.
Increases the size of the critical region.
Increases the probability that the sample will fall into the critical region.
Samples of size n = 16 are selected from a population with μ= 80 with σ= 16. What is the standard error for the distribution of...

...Important Things To Know
* Markup = P-MCP= -1price elasticity of demand
* Market demand = firm’s demand for a monopoly ONLY
* TR=aQ-bQ2 and MR=a-2bQ
* Monopoly output is ALWAYS LESS than competitive output
* Colluding leads to the ideal situation (illegal)
* MC=WMPL
* X=aa+b×MPx or Y=ba+b×MPy
* Y = M/Py – (Px/Py)X
* Isocost Line: C(Q)=wL+rK | Variation: K=TCr-wrL | Slope: -(w/r)
* Isoquant Slope: -(MPL/MPK) | MPLMPK=aKbL=∆K∆L
* Optimal cost-minimization: MRTS=MPLMPK=wr
Questions (word for word from quizzes)
* A firm has market power when it can profitably charge a price that is above its MC
* The more elastic is the demand for a product, the closer is MR to the price
* When a monopolist maximizes its profit by selling a positive amount, its MR = MC at that quantity
* A firm’s markup/price-cost margin is the amount by which its price exceeds its MC, expressed as a percentage of its price
* A firm’s markup over its MC is GREATER the less elastic is the demand curve
* The deadweight loss from monopoly pricing is the amount by which aggregate surplus falls short of its maximum possible value, which is attained in a perfectly competitive market
* A monopolist faces a downward sloping demand curve and by lowering the quantity he sells, he can charge more
* A market is a natural monopoly when a good is produced most economically by one firm
* A loss leader is a product that is sold at a price...

...strategies for growth: ee market penetration, ne market development, en product development,nn diversification downsizing: eliminate products/units that are not profitable/no longer fit the overall strategy
prod and serv lvls of prod core cust. value > actual prod: features, design, packaging, quality, brand name > augmented prod: warranty, after-sale serv., prod support, delivery/credit prod+serv class consumer prod: convenience, shopping, specialty, unsought industrial prod: materials+parts, capital items, supplies+serv. new prod dev: idea generation> idea screening> concept dev+test>mrkting strat dev>business analysis>prod devel>test mrkting>commercialization. npd req’s a customer-centered, team-based + systematic effort. prod. life cycle prod. develop: sales, ^investment, innovators introduction: slow sales, market pioneer. growth: ^ market acceptance, ^ profits, ^ comp. early adopter maturity: v sales, lvl off or v profits, v comp, middle majority decline: v sales, v profits, laggards. plc style:fashion (slow), fad (fast). prod+serv decisions quality: total quality mgmt, performance, conformance, consistency. features, style+design, packag’g, label’g, support serv prod line decisions: length (# of items), filling (+ items within range of line), stretching (lengthens beyond current range ). prod. mix decisions (set of all prod lines + items): width (# of different pls) length (total # of items within pls), depth (# of versions offered of each prod) services mgmt :...

...Kavin Chinnasamy
BADM 375 CheatSheet
Queues form due to variability in arrival times, service times & service availability. Impact of variability increases as utilization increases! (throughput goes up or capacity goes down).
Little’s Law: I = R x T (congestion = arrival rate x delay). Little’s Law is I = R*T (where I = avg inventory, r = throughput rate, t = avg flowtime). Delay explodes as the arrival rate approaches the system capacity: Delay ≈ 1/(capacity–arrival rate).
The utilization (per server): ρ = λ / (s μ). Where λ = arrival rate (also departure rate), s = servers & μ = service rate. For the servers to keep up, we must have ρ < 1.
Queuing models provide measures of approximate long-run performance. Queuing models do not typically provide information about start-up effects. Standard queueing models do not incorporate changes like rush hours – Different models are needed for different times of the day.
The “lost customer” rate = λ x Pb • Effective arrival rate = throughput rate = λ x (1-Pb). The key performance measure is Pb the probability that the system is full & arriving customers cannot get in.
If Cs is the cost per hour per server, & Cw is the cost per hour per customer waiting, then the cost per hour of running a queueing system with s servers is Cs(S) + Cw(i)
Safety Capacity - Capacity carried in excess of expected dem& to cover for system variability. Provides a safety net against higher than expected arrivals or...

...QMS 202 Quiz #1 Crib Sheet
Inferential statistics is the process of using sample results to draw conclusions about the characteristics of a population
Mean: Standard Deviation:
If population of individual measurements is normal, x is normal
Sample size (n ≥ 30), x is normal
To convert any random variable X to standardized normal random variable Z:
To determine the percentile using z-score, use normalcdf(lower, upper, mean, standard deviation).
To determine Z using the given area from the left of the bell curve and standard deviation, use invNorm(probability, mean, standard deviation). If using the right, use invNorm(1 – probability, mean, standard deviation).
Confidence interval when standard deviation is known:
When standard deviation is unknown, use T.
Is population proportion (p) normal? np ≥ 5 and n(1-p) ≥ 5
To determine confidence interval when giving p = x/n, use 1-PropZInt
QMS 202 Quiz #1 Crib Sheet
Inferential statistics is the process of using sample results to draw conclusions about the characteristics of a population
Mean: Standard Deviation:
If population of individual measurements is normal, x is normal
Sample size (n ≥ 30), x is normal
To convert any random variable X to standardized normal random variable Z:
To determine the percentile using z-score, use normalcdf(lower, upper, mean, standard deviation).
To determine Z using the...