Probability
What is the difference between a binomial and geometric distribution?
Binomial distributions have a fixed number of trials but geometric distributions do not.
What is the purpose of the 10% Condition?
To check that trials are approximately independent when sampling without replacement
If a test had a significance level of α = 0.05 and a P-value of 0.03, how would you write your conclusion statement?
Since the P-value of 0.03 is greater than the significance level of α = 0.05, reject H0. We have convincing evidence to suggest (Ha).
1 - alpha (significance level) = this
Confidence %
Why do we say "enough evidence to suggest" in the conclude section of running a test?
We can never definitively conclude something
If 50% of Democrats and 51% of Republicans vote in an election, are party affiliation and likelihood of voting independent?
No - the probability a given voter of a certain party votes in the election changes based on their party affiliation.
Name the four conditions for a binomial distribution
Binary - Each trial is a success/failure
Independence among trials
Number of trials is fixed
Same probability of success for all trials
DAILY DOUBLE
How many tests and intervals are there in total?
13
What is the formula for finding χ2?
Σ (observed - expected)2 / expected
How do you interpret r2?
About r2% of the variation in the y-variable (context) can be explained by the LSRL with the x-variable (context).
If there are 8 black socks, 10 white socks, and 14 gray socks in a drawer, what is the probability of picking out (without replacement) a gray sock, then a black sock, then a white sock?
0.0376
1. Population distribution is approximately Normal
2. Sample data shows no strong skew or outliers
3. n is at least 30 by CLT
Name the tests and/or intervals where df = n - 2
T-test for β and T-interval for β
Z score has standard deviation, T statistic has standard error - standard deviation / n
DAILY DOUBLE
What is the empirical rule?
In a Normal distribution,
68% of values are within 1 SD of the mean
95% of values are within 2 SDs of the mean
99.7% of values are within 3 SDs of the mean
Tyler makes 75% of his free throws. He decides to shoot free throws until he makes four in a row or misses one. What is the probability he attempts four free throws?
0.753 = 0.421875
The probability of Tyler attempting 4 free throws is 0.421875.
DAILY DOUBLE
Which test or interval requires a combined probability?
A 2-Sample z test for difference of proportions
Xaverian believes that on any given day, 12% of its students do not wear their uniform. However, you think this is an exaggeration. You take a random sample of 90 students one day and find that 8 aren't wearing their uniforms.
One-sample z test
What test or interval does this formula correspond to?
(x̄1 - x̄2) ± t* √ [ (s1)2/n1 + (s2)2/n2 ]
A two-sample t interval for μ1 - μ2
What are the names of the teachers from Stats Medic?
Luke and Lindsey
A multiple choice test is scored the following way: No points for a wrong answer, 9 points for a right answer, and 2 points for no answer. If each question has 6 options, how many options should a student eliminate before it would be better to guess than leave the question unanswered?
2 options
Name all five conditions for a Linear Regression test or interval
Linear - Scatter plot shows (+/-) linear relationship between x and y and the residual plot shows no leftover pattern.
Independent - If sampling without replacement, 10% Condition is met.
Random - Random sampling or randomized experiment
Approx Normal - Residual plot shows no strong skew nor outliers OR n is at least 30.
Equal SD - Residual plot shows similar scatter around resid = 0 for each x value.
Is there enough evidence to suggest a difference in daily screen time between husbands and wives? 160 couples were randomly selected and their daily screen times were recorded.
One-sample matched pairs t-test for mean difference
What is the formula if you are trying to find the probability of event A, given event B is happening - P(A|B)?
P (A ∩ B) / P (B)
Name at least 2 of the distribution dinosaurs in Mrs. Hackett's room
Chisquaretops, stegonormalus, t-rexponential, dimetuniformodon