FINAL Flashcards
What is the estimate of a population parameter given by a single number called?
point estimate
What will ALWAYS be the point estimate?
the sample mean
What is a interval estimate for the mean at a specific confidence level?
confidence interval
The 95% CI for the mean is given by what value:
1.96,-1.96
The 99% CI for the mean is given by what value:
2.576, -2.576
The 80% CI for the mean is given by what value:
1.282, -1.282
What are probability mass functions?
Discrete
What are probability density functions?
Continuous
What type of variable takes on an infinite number of values?
Continuous
What is represented by an area under the curve?
Probability
What type of function is the continuous random variable X is a function such that the area under the curve f (x) between any 2 points a and b is equal to the probability that the random variable X takes on an value such that it is P(a<x<b)?
Probability density function (p.d.f)
What does a uniform distribution indicate?
that all values have the same probability
A continuous probability density function ALWAYS satisfies the following 2 conditions:
- f (x) is NEVER EVER NEGATIVE
- The total area under f(x) is ALWAYS 1
What are the 4 qualities of the normal distribution?
- bell-shaped
- symmetrical about mean (u symbol)
- unimodal
- continuous
X ~ N (μ, σ^2) says what?
This distribution is normal
What is the mean and std. dev for a standard normal distribution?
mean of 0; std. dev. of 1
What function is for the random variable X evaluated at the point a that it is defined as the probability that X will take on values less than or equal to A?
cumulative distribution function (cdf)
How do I use the calculator for this type of problem?: P (z <1.28)
- 2nd
- VARS
- NormCDF
- input lower value: any very negative value
- input upper value: value you’re given
- input std. normal distribution mean and sigma
How do I use the calculator for this type of problem?: P(0<z<1.53)
hint: for the endpoints: just use the values you’re given
- 2nd
- VARS
- NormCDF
- input lower value
- input higher value
- input std. normal distribution mean and sigma
How do I use the calculator for this type of problem: P(z>2.13)
- 2nd
- VARS
- NormCDF
- input lower value: given value endpoint
- input higher value: very high positive value
- input std. normal distribution mean and sigma
How do I use the calculator for this type of problem: X ~ N (50,25), find P(X>58.5)
- 2nd
- VARS
- NormCDF
- input lower value: given value endpoint
- input higher value endpoint: high positive value
- Input mean you’re given; input square root of variance you’re given
How do I use the calculator for this type of problem: find P(8.5<x<12)
hint: for the endpoints: just use the values you’re given
- 2nd
- VARS
- NormCDF
- input lower value
- input higher value endpoint
- Input mean you’re given; input square root of variance you’re given
How do I use the calculator for this type of problem:
If X ~ N (25.7, 5.88), what is the minimum value of X required to be in the top 10% of the distribution?
AKA how to find the value that is in a certain percentile?
- 2nd
- VARS
- invNORM
- input (percentile, mean, std. dev)
- tail: left
How do I use the calculator to find for this type of problem: find z .025
1, 2nd
2. VARS
3. InvNORM
4. input (1-percentile, mean std. dev)
5. tail: left
How do I use the calculator to find this type of problem:
Find the probability that an exact amount will be in this interval.
- find the probability of a single prob. being within that range
- 2nd
- VARS
- BinomPDF
- input # trials, probability that correlates, and exact amount you’re trying to find
How do I use the calculator to find this type of problem:
Find the probability that an at most amount will be in this interval.
- find the probability of a single prob. being in that range
- 2nd
- VARS
- BinomCDF
- input # trials, probability that correlates, and exact amount you’re trying to find
How do I use the calculator to find this type of problem:
Find the probability that an at least amount will be in this interval.
same as at most, BUT subtract 1 from the value you get at the end
What is the key difference in finding the exact amount in an interval vs. finding the at most or at least amount?
EXACT amount uses BINOMPDF; EXACT AMOUNT uses BINOMCDF
How do I find the sample standard deviation of the mean (formula):
This is known as the SEM formula
σ/ √n
As n (the sample size increases), what decreases?
STANDARD DEVIATION
What is the new standard error formula?
(√n old / √n new)
What does the central limit theorem tell us?
That if X possesses ANY distribution, with mean and std. deviation, then the sample mean based on samples of size n will have a distribution which is appromixately normal, AS LONG AS n > = 30
What is the central limit theorem z score formula?
Z = (x-μ) / (σ/√n)
Small confidence levels and large confidence levels are not desirable-T or F
False; small confidence levels and LARGE CONFIDENCE LEVELS are desirable
How do I use the calculator to find this type of problem: Find a 99% confidence level for U (T-Interval)
- STAT
- Tests
3.T Interval - Stats
- Input Values
How do I use the calculator to find this type of problem: Gives us list of data*
- STAT
- Calc
- 1-VAR stats
What is the formula for Confidence Intervals?
x̄ n ± z alpha/2 * (s/ √n)
could also be t alpha/2
What is the formula for E?
hint* confidence intervals
z alpha/2 * (s/ √n)
or t alpha/2
What is the formula for Length?
2E
