Unit 3 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 · The 95% interval claim

What does a properly calibrated 95% frequentist confidence procedure mean?

95% of single intervals contain each sample meanAbout 95% of intervals constructed by repetition contain a fixed parameterThe parameter changes between samplesEvery group of 20 intervals includes exactly 19 successes

Question 2 · Unknown population variance

A one-sample t test from 20 independent normal observations has how many degrees of freedom?

18192021

Question 3 · The zero-event problem

Why is a Wald confidence interval [0,0] from zero successes in a small sample suspect?

The event's true probability could still be positiveNo probability model can contain zeroZero successes guarantee the population probability is zeroIt always describes a perfectly unbiased survey

Question 4 · Two sources of variance

Independent groups: sA²=2.5, nA=5; sB²=22, nB=8. Estimate the SE of mean A−mean B.

0.501.803.2524.5

Question 5 · What is paired?

What justifies applying a paired t procedure?

Two unrelated classes of equal sizeThe same persons measured before and after an eventTwo studies published in one journalDifferent measurements simply listed on adjacent rows

Question 6 · Compare two outcome rates

18 of 30 versus 12 of 30 experienced an outcome. What is the risk difference in percentage points?

10203050

Question 7 · The p-value is conditional

For a pre-specified test, p=.03 primarily means what?

The null hypothesis has 3% probability of being trueAssuming the null and other test conditions, results at least this extreme have probability 3%There is a 97% probability of causationThe data were 3% inaccurate

Question 8 · Fair die goodness of fit

Six fair-die expected counts are ten each; observed counts are 15,5,10,10,10,10. Pearson's X²?

02.5510

Question 9 · Table degrees of freedom

For a 3-by-4 independent-count contingency table, the usual chi-square reference has what degrees of freedom?

67121

Question 10 · Power is conditional on an effect

Power 80% for a given alternative means?

There is an 80% chance the null is falseThe test rejects the null in 80% of repetitions under that specified alternativeThe result is 80% accurateThe significance threshold is 80%

Question 11 · Many tests

Twenty independent tests at alpha .05 with all nulls true have what chance of at least one false rejection?

5%20%About 64%95%

Question 12 · Small randomization experiment

For balanced random assignment of four of eight participants to A, how many possible allocations?

81670256

Question 13 · Why replacement is essential

A standard nonparametric bootstrap for a sample mean draws how?

From the empirical sample with replacementAlways from a normal populationFrom the same rows without replacementOnly one observation per replicate