Unit 2 Assessment | Mathematics Project

Practice, not certification. This is an ungraded assessment with no timer, identity requirement, server-side score collection, or claim of educational accreditation. For questions involving real studies, use the stated assumptions.

Question 1 · Simple random sampling

What characterizes a simple random sample of n from N?

Every possible size-n subset has equal selection probabilityOnly volunteers can appearEvery subgroup is equally sizedEvery response is guaranteed unbiased

Question 2 · Stratified design

What is a defining feature of stratified sampling?

Every school is selected as a clusterThe population is partitioned into strata and sampled within themOnly easy-to-reach subjects are usedThe largest stratum is omitted

Question 3 · Cluster dependence

Why can 500 respondents from two schools offer less independent information than 500 separately selected students?

Students in a school may be correlatedAll survey observations are always independentTwo schools cannot contain 500 peopleTheir mean must be zero

Question 4 · At least one success

In three independent fair coin tosses, what is the probability of at least one head?

1/83/87/81

Question 5 · Independence versus exclusion

Can two positive-probability events be both independent and mutually exclusive?

Yes, alwaysOnly when they have equal probabilitiesNo, since the product of positive probabilities cannot equal their zero intersectionOnly for fair dice

Question 6 · Selecting participants

How many four-person groups can be formed from eight distinct people without regard to order?

163270256

Question 7 · Law of total probability

60% use transit. Early commute rates are 30% among users and 10% among nonusers. Overall early commute rate?

10%18%22%30%

Question 8 · Base-rate reasoning

A condition has prevalence 1%, test sensitivity 90%, specificity 95%. What is PPV approximately?

90%95%15.4%1%

Question 9 · The expected outcome

A reward is 8 with probability .25 and 0 otherwise. What is its expected value?

0248

Question 10 · Independent Bernoulli trials

For X~Binomial(40,.25), what is E[X]?

5102030

Question 11 · A count of no events

If X is Poisson with mean 2, P(X=0) is closest to which?

.1353.5.86472

Question 12 · What becomes normal?

The central limit theorem typically concerns the limiting normality of which object under suitable conditions?

The original population observationsA suitably standardized sample meanEvery sample's raw valuesEvery bounded variable automatically

Question 13 · Probability under a density

For X~Uniform(0,2), what is P(.5<X<1.5)?

0.25.51