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...

...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...

...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,...

...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...

...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:...

...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 ≈...

...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)....