MATH&146 Lesson 8 - Bootstrap Intervals for One Proportion

Flashcards reviewing key concepts, definitions, case studies, and bootstrap confidence intervals for one proportion from Lesson 8.

What are the primary concerns of hypothesis tests versus confidence intervals in statistical inference?

Hypothesis tests are used to test a claim and attempt to answer a simple yes/no research question, whereas confidence intervals are used to estimate the unknown value of a population parameter.

In statistics, what is the difference between a parameter and a point estimate?

A parameter is the true, unknown value of interest from a population, while a point estimate is the sample's estimate that serves as the best guess for that parameter.

In the medical consultant study, what was the consultant's point estimate ($\hat{p}$) based on $3$ complications in $62$ surgeries?

The point estimate is $\hat{p} = \frac{3}{62} \approx 0.0484$ (or approximately $4.84\%$).

Why could the medical consultant study not establish a causal connection between using a consultant and lower complication rates?

The study was observational, meaning confounding variables—such as patients who afford a consultant also being able to afford better overall medical care—could not be ruled out.

What is bootstrapping in the context of statistical inference?

Bootstrapping is a method of sampling with replacement from the observed sample dataset to approximate the variability of sample statistics (such as $\hat{p}$) across repeated samples.

How is the medical consultant dataset represented in a physical resample marble model?

It is represented as a bag with $3$ red marbles (complications) and $59$ white marbles (no complications), from which $62$ marbles are drawn one at a time with replacement.

What was the middle $95\%$ bootstrap percentile confidence interval for the medical consultant's complication rate?

The range of $95\%$ of the bootstrapped values spanned from $0\%$ to $11.3\%$.

Does the $0\%$ to $11.3\%$ confidence interval prove that the medical consultant's complication rate is lower than the national average of $10\%$?

No, because the interval contains $10\%$ (overlapping it), meaning the true rate could be higher or lower than $10\%$, and observational data cannot demonstrate causation.

Who authored the textbook Statistics: Unlocking the Power of Data, which StatKey accompanies?

StatKey was created by Lock, Lock, Lock, Lock, and Lock.

How is a middle $95\%$ bootstrap confidence interval obtained using StatKey for a single proportion?

Click "CI for Single Proportion", enter the count and sample size in "Edit Data", generate bootstrap samples, and check the "Two-Tail" option to display the $2.5\text{th}$ and $97.5\text{th}$ percentiles.

In Elizabeth Newton's 1990 study at Stanford University, what point estimate ($\hat{p}$) was observed for listeners guessing the tune correctly?

Out of $120$ listeners, $3$ guessed correctly, yielding a point estimate of $\hat{p} = \frac{3}{120} = 0.025$ (or $2.5\%$).

What was the $95\%$ bootstrap confidence interval for the proportion of listeners guessing the tune in Elizabeth Newton's study?

Across $10,000$ computer simulations, the $95\%$ interval ranged from $0.000$ to $0.0583$ (or $0\%$ to $5.83\%$).

What is the "curse of knowledge" as demonstrated by the tappers-and-listeners experiment?

It is the phenomenon where the more familiar you are with information, the harder it is to put yourself in the mindset of someone who does not possess that information.

According to the United States Geological Survey (USGS), what percentage of Earth's surface is covered by water?

About $71\%$ of the Earth is covered by water.