Final Exam Stat 1430

if p-value = alpha

"marginal result"

what is the derivative of e^-x

-e^-x

e^-1 =

1/e

what is the notation for coefficient of determination

R-Sq

type 1 error

Rejecting null hypothesis when it is true - false alarm - ex: your yogurt might have been ok and you said it wasn't

what does "Sy" stand for?

SD of y values

Sigma Xbar

SigmaX / sqrt.(n)

variance of a discrete random variable

Weighted average of the squared deviations from the mean - notation: sigma - doesn't use units

If X is a binomial random variable then X is also a __________________ random variable.

discrete finite

population

entire group of interest

probability density function of a continuous random variable

f(x) function that tells you how much probability is in the area near x. (not on x, around it)

if p-value > alpha

fail to reject Ho

type 2 error

failing to reject a false null hypothesis - the yogurt might not be filling correctly but you didn't detect it - more complex than type 1 error

Suppose the correlation between two variables X and Y is .8. That means the correlation between Y and X is -.8. (true/false)

false

Suppose the correlation between yards rushing and yards passing is .6. That means the correlation between feet rushing and feet passing is .6 x 12 (since you multiply yards by 12 to convert to feet). (true/false)

false

uniform distribution means

flat

what type of correlation is -1

perfect downhill

what type of correlation is + 1

perfect uphill

With a continuous random variable, P(a < X < b) is the area under the curve f(x) between a and b. (true/false)

true

If x is continuous then P(x < 4) = P(x <= 4). (true/false)?

true because the probability of x=4 is 0.

outliers affect confidence interval (true/false)

true because they affect the mean

what type of correlation is +- .3

weak linear relationship

the mean of a discrete random variable

weighted average of the possible outcomes; weights are the probabilities mu x = sum of x p(x)

use _______ to predict _________

x , y

coefficient of determination

% of variability in y that is due to x

confidence level=

(1 - alpha) %

characteristics of a continuous random variable

- X is a continuous random variable if it takes on values that are in an interval on the real number line uncountably infinite

how to find the best line

- smallest SSE - find the values of b0 and b1 that minimize SSE

Central Limit Theorem (CLT)

If X has any distribution (not normal) then the SHAPE of the sampling distribution of Xbar is approximately normal, as long as n > 30

Mxbar =

Mx

what does "Sx" stand for?

SD of x values

how should you round when your finding sample size

always round up

sampling distribution

finding the distribution of all possible values of the sample statistic (from all possible samples of size n)

discrete random variable

finite or countably infinite ex: number of flips till 100 heads - x = 0, 1, 2, 3, ......

if you switch x and y in a regression problem, does the correlation change?

no

what type of correlation is 0

no linear relationship

if X has a normal distribution. the shape of the distribution of X is _______________ and the shape of the sampling distribution is _______________

normal; normal

if X does not have a normal distribution. the shape of the distribution of X is _______________ and the shape of the sampling distribution is _______________

not normal; approximately normal if n is large enough

what are the 2 conditions n needs to meet to use z

np >= 10 n(1-p) >= 10

b1=

slope

Correlation is affected by outliers (true/false)

true

b0=

y-intercept

best line formula =

y^ = b0 + b1x

can you have a high level of confidence but a small MOE?

yes, bc Z can increase based on the high level of confidence so as increase in n bring MOE down

If X is a continuous random variable, then p(x) = ___________ for any value of x. why?

0 because there is no area or probability at any single point

what is e^0

1

probability distribution of a discrete random variable 2 requirements:

1. 0 <= P(x) <= 1 2. sum of P(x) = 1

probability density function of a continuous random variable 2 requirements:

1. f(x) >= 0 2. total area under the curve = 1

what are the 2 conditions you need to check for confidence interval

1. np hat >= 10 2. n(1 - p hat) >= 10

what are the 5 properties of correlation

1. quantitative variables only 2. linear relationship only 3. no units 4. if you switch x and y you get the same correlation 5. affected by outliers and skewness

to be 90% confident add and subtract ___________ standard errors

1.645

to be 95% confident add and subtract ___________ standard errors

1.96

Suppose X has a uniform distribution on the interval [0, 10]. What is f(x)?

1/10

Let f(x) = kx where x is between 0 and 2. What is the value of k that makes this a legitimate density function?

1/2

to be 99% confident add and subtract ___________ standard errors

2.58

Selling price = $5,240 + $33.80 (Number of Square Feet). How do you interpret the slope for this equation?

As square feet increase by 1, selling price increases by $33.80

how to get the formula for sample size

Xbar +- Z(sigmax/sqrt.n) = desired value of MOE*

random variable

a characteristic you can measure, count, or categorize

what does "observed y" mean?

a data point

Suppose the equation y = 3.45 - 2.58x represents a valid regression equation and X can be used to predict Y. From this information, we know that X and Y have _____________ correlation.

a negative

statistic

a number that describes the sample ex: sample mean (X bar)

parameter

a number that summarizes the population ex: pop mean

sample

a subset of the population that you select

SD of a discrete random variable

a weighted average of the deviation from the mean

best y-intercept formula =

b0 = ybar - b1 (xbar)

best slope formula

b1 = r (sy/sx)

why do you want to choose the sample size beforehand?

bc you don't want surprises with the MOE

If a residual is negative, then that data point lies _________________ the regression line.

below

if the problem asks you to "estimate" what are you trying to find?

confidence interval

What factors affect margin of error?

confidence level sample (size) population SD

is Time continuous or discrete

continuous

when n increases, MOE ____________

decreases

Your boss gives you the following regression equation. X = square feet and Y = selling price Selling price = $5,240 + $33.80 x Does it make sense to interpret the Y-intercept for this equation? (true/false)

false

when the pop SD increases, MOE _____________

increases

when the confidence level increases, Z ____________ and MOE _______

increases, increases

continuous random variable

infinite number of possibilities (uncountably infinite) ex: wait 10 minutes and then you're going to leave

percentile

kth percentile is the value of x where k% lies below x

probability distribution of a discrete random variable

list of all the possible values of x and how often you expect them to occur (looking into future)

how does outliers and skewness affect correlation

makes the relationship weaker (lower)

what does y bar stand for

mean/average of y-values

what type of correlation is +- .5

moderate linear relationship

what type of correlation is +- .6

moderately strong linear relationship

what is the Notation for the mean of a Continuous Random Variable

mu x

mu (x + y) =

mu x + mu y

Residual=

observed y - predicted y

residual=

observed y - predicted y

p-value

probability of being beyond the test statistic

if p-value < alpha

reject Ho

what does "r" stand for

sample correlation

the CLT only pertains to the ____________ of the distribution of the random variable Xbar

shape

spread

standard error/standard deviation

what type of correlation is +- .7

strong linear relationship

SSE stands for

sum of squares for error

significance level

the pre-set cut-off value before you collect any data - usually 0.05 - ALPHA

confidence interval

the range of values within which a population parameter is estimated to lie

what does correlation measure?

the strength and direction of linear relationships

If X and Y are independent, then True/False: Variance of (X-Y) = Variance of (Y-X)

true

Suppose X has a uniform distribution on the interval [0, 10]. True or false, the mean of X is 5.

true

linear transformation formula

y = ax + b mu y = a (mu x) + b