Probability
What is the probability of getting an ace (any kind) in a standard deck of cards.
4/52
What is SRS?
Simple Random Sample.
When do we use a T curve instead of a Z?
When sigma is unknown.
What's the general format of a confidence interval?
Point estimate ± margin of error
What does the null hypothesis usually say?
No effect/no difference
P(ace of spades OR ace of hearts)
2/52 = 1/16
Name any 2 sampling bias.
1) Convenience Sampling
2) Response Bias
3) Voluntary Response Bias
4) Undercoverage Bias
5) Non-response Bias
Any 2 among the 5 will be correct.
A distribution has a long tail stretching to the right. Skewed left or skewed right?
Skewed Right(Positive Skew)
If you raise your confidence level from 90% to 99%, does the interval get wider or narrower?
Wider
What does a p-value actually tell you?
The probability of getting results at least as extreme as yours, assuming the null is true.
Draw 3 cards without replacement; P(getting a king, an ace, and a jack, any order)
(4×4×4) / C(52,3) = 64/22,100 ≈ 0.0029
A school district wants to test a new math curriculum. They randomly select 5 elementary schools from the district and test every 4th grader in those 5 schools. What type of sampling is this?
Cluster Sampling.
In a right skewed distribution, which is larger, the mean or the median?
The mean
Name 2 ways to shrink the margin of error.
Increase the sample size, and lower the confidence level.
p-value = 0.03, α = 0.05. Reject or fail to reject?
Reject the null (since 0.03 < 0.05).
Without replacement, P(ace first, king second, jack third)
4/52 × 4/51 × 4/50 ≈ 0.00048
A researcher wants to know how local residents feel about a new park tax. They stand outside a high-end luxury gym at 10:00 AM on a Tuesday and interview the first 50 people who walk out. What type of bias is present.
Convenience Bias.
Test Scores are N(80,5). About what % of scores fall between 70 and 90?
95% (within 2SD)
A sample of 100 students has a mean study time of 3 hours and a standard error of 0.2 hours. Give a rough 95% CI (use z* ≈ 2)
3 ± 2(0.2) = (2.6, 3.4) hours.
What's a Type I error vs a Type II error?
Type I = rejecting a true null (false positive). Type II = failing to reject a false null (false negative).
Without replacement, P(ace of spades, then king of clubs, then jack of diamonds)
1/52 × 1/51 × 1/50 = 1/132,600 ≈ 0.0000075
very low :)
To sample 20 students, a teacher splits her class of 40 into 20 boys and 20 girls. She flips a coin: heads, she chooses all 20 boys; tails, she chooses all 20 girls. Why this method is NOT a Simple Random Sample.
Every possible group of 20 students does not have an equal chance of being selected.
Heights are N(65, 3) inches. What % of people are taller than 71 inches?
z = (71−65)/3 = 2, so ~2.5%.
A 95% CI for mean student height is (64, 68) inches. Write a correct interpretation.
We are 95% confident that the true mean height of all students is between 64 and 68 inches.
A chip company claims bags average 100g. A test gives p = 0.002 at α = 0.05. State the conclusion in context.
Reject the null there's convincing evidence the true mean weight is different from 100g.