Sampling & Experiments
Interpretations
Mixed Bag
Probability Rules!
Normal Distribution
100
Neither the subject nor those who measure the reponse variable know which treatment a subject received.
A double-blind experiment
100
P(x ≥ 4) = ?, where x is the number of chocolate bars eaten on Halloween.
The probability that the number of chocolate bars eaten is at least 4.
100
How to identify outliers for univariate data
Q1 - 1.5(IQR) and Q3 + 1.5(IQR)
100
The probability of rolling a fair die three times and getting three fours (show work).
P(rolling three 4s) = P(4)*P(4)*P(4) = P(4)^3 = 1/216
100
Write the values for the empirical rule (what are the percentages)?
68-95-99.7
200
A common form of blocking for comparing just two treatments.
Matched Pairs
200
Interpret the 4 values below:
normcdf(-1E99, 81, 80, 2).
Lower bound, upper bound, mean, and SD
200
How to calculate the expected value of a discrete random variable
The mean of the random variable found by summing the products of the values of x and their respective probabilities
200
The probability of pulling a red or queen from a standard deck of cards (show work).
P(red or queen) = P(red) + P(queen) - P(red and queen) = 26/52 + 4/52 - 2/52 = 28/52 = 7/13
200
Women’s heights have a mean of 64.8 in. and a standard deviation of 2.5 inches. Find the z score corresponding to a woman with a height of 70 inches and determine whether the height is unusual compared to the average height.
Z = 2.08
300
When some groups in the population are left out of the process of choosing a sample
Undercoverage
300
Interpret the z-score of -3.45
The data value is 3.45 standard deviations below the mean
300
Two events are this if they share no common outcome.
Mutually exclusive
300
A coin is tossed three times. What is the probability that it lands on heads exactly one time?
0.375
300
For the verbal portion of this SAT, the mean was 425 and the standard deviation was 110. Based on this information what percentage of students would be expected to score between 350 and 550? Assume the data is normally distributed.
62.45% of the students would be expected to score between 350 and 550 on their verbal SAT.
400
The population is divided into groups. A set number of groups are randomly selected and all individuals in the chosen groups are sampled.
Cluster Sampling
400
Interpret the relationship between the mean and median in this distribution.
Mean > Median
400
How to determine if two events, A and B, are independent
P(B|A) = P(B) or P(A|B) = P(A) or
P(A and B) = P(A)P(B)
400
Jess is a high school softball player. She gets a hit 70% of the time. That means her average is .70. What is the probability that she gets her first hit on her fifth at bat?
0.0057
400
The marks in a test are normally distributed with a standard deviation of 20%. If the top 10% of students score more than 90%, what is the mean test mark?
z = 1.282, and μ = 64.4%
500
The effects of two variables on the response cannot be distinguished from each other.
Confounding
500
The impact of conducting an experiment using random selection AND random assignment.
Random selection --> generalize to population
Random assignment --> cause and effect
500
How to calculate the standard deviation of the difference between two random variables.
The square root of the sum of the variances of the two random variables
500
The formula for finding the probability of someone liking Taylor Swift given that they are an AP Stat student.
P(TSwift|AP Stat Student) = P(TSwift Fan and AP Stat Student)/P(AP Stat Student)
500
The heights of Great Spotted Kiwi Birds are normally distributed. The shortest 10% are under 44 cm tall and the tallest 20% are more than 48 cm tall. Calculate the mean and standard deviation of the kiwi’s heights.
-1.281𝜎 = 44 − 𝜇 and 0.842𝜎 = 48 − 𝜇
σ = 1.884 and μ = 46.4