Test That Significance!
A survey of 100 randomly selected students from Loomis was conducted and found that 0.9 students are going on vacation this summer.
Which of the 3 conditions does this fail?
1. Random - Good
2. 10% condition - Fails! 100 > 10% of 750.
3. Large counts - Good
What is the z* critical value for an 80% confidence level?
1.28
Define the Central Limit Theorem
When n>30, the sampling distribution is approximately normal.
The first English settlement of the Connecticut Colony, settled in 1633
Windsor!
Never heard of self care
Half your brain just aint there
Manchild - Sabrina Carpenter
1-sample z test for p
H0: p1 = 0.5, HA: p1 < 0.5
p-hat = 40/100 = 0.4
p-value?
p-value = 0.0228
1-sample z interval for p, CL = 95%
p-hat = 40/100 = 0.4
Interval?
(0.304, 0.496)
More statistical words for x and y variables
Explanatory and Response Variables
This is the oldest continuously operating amusement park in the USA and is home to the famous wooden roller coasters Boulder Dash and Wildcat
Lake Compounce
If the world was ending, I'd wanna be next to you
If the party was over and our time on Earth was through
Die With a Smile - Lady Gaga, Bruno Mars
2-sample z test for p
H0: p1 = p2, HA: p1 > p2
p-hat1 = 33/50 = 0.66
p-hat2 = 28/50 = 0.56
p-value?
p-value = 0.1527
2-sample z interval for p, CL = 95%
p-hat1 = 20/50 = 0.4
p-hat2 = 40/50 = 0.8
Conclusion? Is there a difference?
We are 95% confident that the interval (-0.575, -0.225) contains the true proportion.
Convincing evidence p1 < p2.
p(A|B) = ?
p(A|B) = p(A and B) / p(B)
Groton, CT is known for building the first of this kind of war machine
Nuclear Submarine
How can you look at me and pretend
I'm someone you've never met?
back to friends - sombr
1-sample z test for p, alpha = 0.05
H0: p = 0.8, HA: p != 0.8
p-hat = 30/40 = 0.75
Conclusion?
Assuming H0 is true, p-value is 0.4292
B/c p-value > alpha, fail to reject H0!
2-sample z interval for p, CL = 99%
p-hat1 = 30/50 = 0.6
p-hat2 = 60/75 = 0.8
Conclusion? Is there a difference?
We are 99% confident that the interval (-0.41, 0.01) captures true difference in proportion.
No convincing evidence there is a difference!
The four conditions for a binomial distribution
1. Binary
2. Independent
3. Number of trials is fixed (n=_)
4. Same probability of success (p=_)
This motto triggered New Yorkers when it appeared on the Welcome to Connecticut sign on I-95
Home of the Pizza Capital of the United States
Si te quieres divertir
Con encanto y con primor
Solo tienes que vivir
NuevaYol - Bad Bunny
2-sample z test for p, alpha = 0.01
H0: p1 = p2, HA: p1 != p2
p-hat1 = 30/50 = 0.6
p-hat2 = 60/75 = 0.8
Conclusion?
Assuming H0 is true, the p-value is 0.0147.
B/c p-value > alpha, fail to reject H0!
1-sample z interval for p, CL = 88%
p-hat = 30/40 = 0.75
Conclusion?
We are 88% confident that the interval (0.644, 0.856) captures true proportion.
The four principles of a well-designed experiment
1. Comparison
2. Random Assignment
3. Replication
4. Control
What makes the highest point in CT unique (and kind of embarassing)?
It is located on the slope of a mountain that peaks in Massachusetts
I break her heart, Comme Garcon
Put on a shirt, get put on a blimp
Timeless - The Weeknd, Playboi Carti