An analyst has a sample of 50 website session durations and wants a 95% confidence interval for the mean session duration. The data are highly skewed and the sample size is small. The analyst generates 10,000 bootstrap samples and computes the mean for each. Which method should the analyst use to construct the confidence interval?

Use the original sample mean plus or minus 1.96 times the sample standard deviation divided by the square root of 50

Take the mean of the bootstrap means plus or minus 1.96 times their standard deviation

Take the 2.5th and 97.5th percentiles of the original sample data

Sort the 10,000 bootstrap means and take the 250th and 9,750th values as the interval endpoints

How is the bias of a statistic estimated using bootstrapping?

By computing the standard deviation of the bootstrap distribution

By taking the difference between the maximum and minimum bootstrap statistics

By comparing the bootstrap distribution to a normal distribution

By subtracting the original sample statistic from the mean of the bootstrap distribution

A real estate analyst builds a linear regression model to predict house prices using square footage and number of bedrooms. The analyst notices that the two predictors are highly correlated (r = 0.9). Which consequence is most likely?

The R-squared will be artificially inflated

The predictions will be biased for new data

The coefficient estimates will be unbiased but have large standard errors

The model will always overfit the training data

In which situation is bootstrapping most appropriate?

When the original sample is a random sample from the population and the statistic is the sample mean

When the sampling distribution of a statistic is unknown or difficult to derive analytically

When the sample is very small and the population distribution is known to be normal

When the goal is to test a hypothesis about the population mean with a known standard deviation

Why does bootstrapping rely on sampling with replacement rather than without replacement?

To allow the same observation to appear multiple times, mimicking the process of sampling from a larger population

To guarantee that the bootstrap distribution exactly matches the original sample's distribution

To reduce the sample size of each bootstrap sample, making computation faster

To ensure each bootstrap sample is an independent random sample from the population

Python InstitutePCAD - Certified Associate in Data Analytics with Python

Domain 3Objective 2

Inferential Statistics PCAD-31 Practice Questions (Page 5)

Part of the Statistical Analysis domain, which accounts for 8.3% of the PCAD-31 exam. Python Institute does not publish an official question count, but from its 60-minute exam (~25–40 total, ~2–2 in this domain), expect 1–1 from this objective — we provide 33 practice questions to prepare you well beyond it. (estimate)

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Questions 21–25

21application · medium
An analyst has a sample of 50 website session durations and wants a 95% confidence interval for the mean session duration. The data are highly skewed and the sample size is small. The analyst generates 10,000 bootstrap samples and computes the mean for each. Which method should the analyst use to construct the confidence interval?
Select an answer first
22foundation · easy
How is the bias of a statistic estimated using bootstrapping?
Select an answer first
23expert · hard
A real estate analyst builds a linear regression model to predict house prices using square footage and number of bedrooms. The analyst notices that the two predictors are highly correlated (r = 0.9). Which consequence is most likely?
Select an answer first
24foundation · easy
In which situation is bootstrapping most appropriate?
Select an answer first
25foundation · easy
Why does bootstrapping rely on sampling with replacement rather than without replacement?
Select an answer first

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