The Basics
P:Population Proportions
What is the parameter we estimate with these confidence intervals and significance tests?
Simple Random Sample refers to a sampling method that has the following properties. The population consists of N objects. The sample consists of n objects. All possible samples of n objects are equally likely to occur. The last condition is fulfilled through some order of randomization.
What is the Random?
1. State: We want to estimate the true- P of -population in context- at a/an-% confidence level 2. Plan: give the type of interval Conditions: SRS Normality Independence 3. Do: test statistic and interval calculations 4. Conclusion: We are -% confident that the true P of population in context- is between - and - (units).
The value we use to decide if we reject the null or not.
What is alpha?
Splitting a population into groups and then taking an SRS of each group.
What is systematic sampling?
CI=Point Estimate +/- Margin of Error
What is the general formula form confidence intervals?
The conditions for one-proportion z-interval
What are The Random, 10% condition and np≥10, n(1-p)≥10?
Derive this from the margin of error
What is finding the sample size?
The probability that you make the correct decision when you reject the null hypothesis given a value for the alternative.
What is power?
68-95-99.7
What is the empirical rule?
n≥30; the means of repeated samples will tend to follow a Normal distribution if the sample size is large enough
What is the central limit theorem?
2-Sample proportion z-Test-Random, 10% condition, Normality: n1pc≥10, n1(1-pc)≥10, n2pc≥10, n2(1-pc)≥10
2-Sample proportion z-Interval- Same as the conditions for the 2-sample proportion z-interval, but with the proportion statistics rather than the PHAT combined.
What are the conditions for two- sample proportions intervals and tests?
The hypothesis, which in a significance test, we try to disprove or reject.
What is the null hypothesis?
The probability the given the null hypothesis is true, that we get a sample proportion as extreme or more extreme.
What is the p-value?
P (A and B) / P(B)
What is the formula for conditional probability?
z scores, they indicate the confidence level
What are critical values? What are they used for?
To infer on the population
Why do we check for randomness?
When you reject the null when the null is true
What is a Type I error?
When you have to double your p-value.
What is a two sided test?
Sqrt ( n * p * (1 - p))
What is the formula for standard deviation of a binomial distribution?
1 - Power
What is the P(type II error)?
To be able to calculate the standard deviation
Why do we check the 10% condition?
2.576
What is the z score/critical value for a 99% CI?
H0: p = 0.5
Ha: p > 0.5
p - hat: 17/30
z=?
What is 0.73?
1 / p
What is the expected value of a geometric distribution?