Sampling & Experiments
Neither the subject nor those who measure the reponse variable know which treatment a subject received.
double-blind experiment
P-value = 0.001
the probability of seeing results at least as extreme as those observed, assuming the null hypothesis is true, is 0.001
How to identify outliers for univariate data
Q1 - 1.5(IQR)
and
Q3 + 1.5(IQR)
the probability of rolling a fair die three times and getting three fours.
P(rolling three 4s) =
P(4)*P(4)*P(4) = (1/6)^3=0.0046
Lylah created an app, and she recently updated the app. She randomly samples a group of users to estimate what percentage of all users are using the updated version.
1 proportion Z interval
A common form of blocking for comparing just two treatments.
matched pairs
Interpret the slope of the least squares regression line given by
hat(y)=38.3+1.43x
where y=height in inches and x=footlength, in inches
For every one inch increase in the footlength, we predict a 1.43 inch increase in height
The expected value of a discrete random variable from a table
Multiply down and add across
A factory finds that 10% of products are defective.
Find the probability that the first defective item is found within the first 5 items.
Geometric cdf
p=0.1
trials=5
0.40951
A food scientist wants to estimate the difference between the weights of eggs classified as jumbo and large. They plan on taking a sample of eggs of each type and comparing the average weight between the samples.
2 sample t interval
When some groups in the population are left out of the process of choosing a sample
undercoverage
A z-score of -3.45
The data value is 3.45 standard deviations below the mean
How to determine if two events, A and B, are independent
P(B|A) = P(B) or P(A and B) = P(A)P(B)
What should you do if the question about probability has the word "given" or "if _____"
cover up the part of the table that is irrelevant
A market researcher wondered if there was a relationship between a person's age and which media streaming service they preferred. The researcher obtained a random sample of people and categorized each of them as a teen or adult. They also categorized each person based on their preferred streaming service.
chi square test of independence
The population is divided into groups. Some groups are randomly selected and all individuals in the chosen groups are sampled.
cluster sampling
Interpretation of 95% Confidence level for the population proportion of Loyola students who drive an SUV is (0.045, 0.086)
We are 95% confident that the true proportion of Loyola students who drive an SUV is between 4.5% to 8.6%
The standard deviation of the difference between two random variables.
the square root of the sum of the variances of the two random variables
VARIANCES ADD!
What key word tells you to use pdf (geompdf or binompdf)?
exactly
Paulo works at the United Nations. He researched what percent of the world's population lives on each continent. He surveys a sample of employees at the United Nations about their continent of origin to see if the distribution in the sample agrees with the percentages he researched.
The effects of two variables on the response cannot be distinguished from each other.
confounding
The 95% confidence interval (-4.25, -1.33) for the difference of two means (mean #1 - mean #2).
We are 95% confident that mean #1 is between 4.25 and 1.33 units less than mean #2"
Calculating a Z -score
z=(x-mu)/sigma
What is the probability of at least 3 defective items in a batch of 20 items if the defect rate is 5%?
binom cdf
trials: 20
p: 0.05
x value: 2
then subtract from 1
0.075
Rex wants to estimate the average finishing time of the approximately 50,000 finishers at the New York City Marathon. He takes a random sample of finishers and records their times.
1 sample t interval