Chapter 6
Two of the Four conditions for a Binomial Distribution are (BINS)
Binomial (two outcomes per trial), Independence (between trials), Number (of trials is fixed), Success (of each trial is fixed)
This modifier of your confidence interval is related to the strength of your confidence interval, by relating the width of your confidence interval to the width of the normal distribution.
The confidence associated z-score
This is the hypothesis that the results we see in our study are a result of the sampling variability which naturally arises from the randomness in our sampling method.
The Null Hypothesis
This scientific philosopher believed that Science was by definition that which could be questioned. Its his view of Science that is most commonly held today.
Sir Francis Bacon
If two events cannot occur at the same time, they are called this.
Mutually Exclusive
Your friends play a game, where you guess their birthday. You keep guessing until you get it right, and count the number of tries it takes. Why is this not a Geometric Distribution?
Because the probability of success for each trial changes.
The formula for the standard error of a confidence interval in a proportional sampling distribution.
sqrt((p(1 - p)/n)
This is the hypothesis which is representative of the idea that the underlying phenomena we're studying is responsible for the results we obtain in our study.
Alternative Hypothesis
This theorem states that all sampling distributions become approximately normal as the number of samples increases above 30.
The Central Limit Theorem.
The Law of Averages.
Two of the Four conditions for Geometric Distribution (BITS)
Binomial (two outcomes), Independence (between trials), Trials (the goal is to count the number of trials that occurs before a success), Success (probability on each trial remains the same)
Sample size between 15 and 30
Sample size less than 1/10th of the population of interest
Sample must be approximately normally distributed.
2 requirements for statistical analysis of a z-distribution statistical significance test.
The number of trials must be less than 1/10th of the population of interest.
This sampling distribution is useful for sampling distributions of trials between 15 and 30. However, you must be careful to ensure normality, as the Central Limit Theorem does not apply!
t-distribution (Students distribution)
What is the name of this theorem for checking independence between two categorical variables using Probability?
Bayes Theorem
Give two examples of a Binomial Probability Distribution.
1 - Flipping a number of coins, and counting the number of heads
2 - Shooting a number of basketballs, and counting how many of them go in
3 - Going up to bat a number of times in baseball, and counting how many of those at bats lead to on base.
2 requirements for a proportional confidence interval
Sample size must be greater than 30.
Sample size must be less than 1/10th of the population of interest.
Number of successes (np) must be greater than 10
Number of failures (n(1-p)) must be greater than 10.
In a case where a Type 1 error would be relatively catastrophic, what actions should be taken?
The alpha level should be lowered.
If a statistical analysis is said to hold relatively true, even if the conditions for analysis are not entirely met, the analysis is said to be this.
Robust
If you multiply the probability of every event in a discrete probability distribution by its outcome, and then divide by the number of events, you get this value.
The Expected Value of the Probability Distribution.
Continuous versus Discrete.
What is the 95% confidence interval for a sampling distribution with a mean of 0 and a standard deviation of 1?
Any statistical significance test can be manufactured to have a significant p-value by increasing the number of trials large enough. Just because a test is statistically significant doesn't mean that it is this.
Practically significant.
The standard deviation is a measure of this aspect of a sampling or probability distribution.
The spread.
The Law of Large Numbers.