Key Terms
This is the process of generalizing or predicting information that was obtained from a sample from a population.
What is inferential statistics?
What is the cutoff for an unusual probability?
Bonus! Give me examples of what doesn't count as a probability.
Less than 0.05
What's the formula for calculating the z-score for both the sample and population? Please write down answers on the board
I will check answers on the board.
What's the difference between a Type I and Type II error?
Bonus! Write down the symbols for the probability of these errors.
For Type I, you reject the null hypothesis when it really was true.
For Type II, you fail to reject the null hypothesis when the alternative hypothesis was true.
How to draw boxplots and summary data?
Graph-->boxplot
Stats-->summary stats
The Central Limit Theorem
This theorem states that as the sample size of a population increases, then the more normal the sampling distribution becomes, regardless of the shape of the original population.
What does it mean if two events are mutually exclusive?
Sadie has recorded the data of the time it takes for dogs in her shop to get groomed. The results are normally distributed with a mean of 32 minutes and a standard deviation of 7 minutes. Customers get charged more if the grooming takes at least 45 minutes. What percentage of customers pay more?
How does the sample size affect the margin of error? The confidence interval?
As sample size increases, the margin of error decreases.
As the sample size increases, the confidence interval gets narrower.
How do I calculate sample size? Bonus, what's the formula to calculate width?
Stats-->Z-stats-->One-sample--> Width/Sample size
Width= 2*E
What is the difference between theoretical and experimental probability?
Theoretical probability is where you do calculations and all the outcomes are equally likely.
In experimental probability, you observe the outcome through an actual experiment.
Medical Testing: Antibody prevalence= 4% Test accuracy= 97%
Please work out the solution on the board:)
True positive= 388/ 0.039
False negative=12 /0.001
True negative= 9312/0.931
False positive= 288/0.029
Draw the Empirical Rule
Good Job!
How do we tell t-distributions from z-distributions?
Bonus points if you tell me what the similarities are between them.
T-distributions are used when we do not know the standard deviation of the population. There is also more area within the tails compared to z-distributions. They both are centered/symmetric at 0 and have an area of 1.
How do I find out the area within the area of a normal curve?
Stats--> Calculator--> Normal
What are the null and alternative hypotheses? Bonus points if you can tell me what word the null hypothesis is known as
The null hypothesis is the statement of no change or difference to be tested. It is assumed until evidence proves otherwise. Also known as the "status quo."
The alternative hypothesis is the statement we are trying to find evidence to support.
In a standard deck of cards, what's the probability that you draw a red card, given that it's a heart?
13/52= 0.25
Sadie takes a sample of 20 dogs to record the time it takes to groom them. The mean is 32 minutes, and the standard deviation is 7 minutes. What is the sample mean and standard deviation?
Sample mean= 32 Standard deviation=1.565
Do we ever accept the null hypothesis? Why?
No, because we don't have access to the full population and don't know the exact value stated in the null. This is similar to what we do in the court system.
What are the steps to calculating confidence interval?
Stats-->T-Stats-->One Sample-->With summary/data (select column, choose confidence interval or optional graph)
As you do more observations while conducting an experiment, the closer that observed probability will get to the actual probability.
What is The Law of Large Numbers?
In a standard deck of cards, what's the probability that you will draw at least one spade?
52-13=39--> 39/52=0.75 --> 1-0.75= 0.25
What's the effect of sample size on proximity from the mean?
As sample size increases, the probability of being near the mean also increases.
Prof. Gump's class average was an 83%. She believes that this has changed since they just had an exam. The null hypothesis was rejected. Write the conclusion for this.
Bonus points if you write down the null and alternative hypotheses.
There is sufficient evidence to conclude that the mean grade average of Prof. Gump's class is different from 0.83.
How to calculate z-score?
Stats-->Calculator--> Normal-->find the probability on the normal distribution, then use that probability on a z-curve (mean=0, std dev=1)