Confidence intervals in R Programming - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a confidence interval?

A confidence interval is a range of values that likely contains the true value of a population parameter. It shows how sure we are about an estimate from sample data.

beginner

In R, which function is commonly used to calculate a confidence interval for the mean of a numeric vector?

You can use the t.test() function on the numeric vector. It returns a confidence interval for the mean by default.

beginner

What does a 95% confidence interval mean in simple terms?

It means if we repeat the sampling many times, about 95% of those intervals will contain the true population value.

intermediate

How do you interpret a confidence interval that is very wide?

A wide confidence interval means there is more uncertainty about the estimate. It can happen with small samples or high data variability.

intermediate

Write a simple R code snippet to calculate a 99% confidence interval for the mean of a numeric vector data.

result <- t.test(data, conf.level = 0.99) result$conf.int This code runs a t-test and extracts the 99% confidence interval for the mean.

What does the confidence level (e.g., 95%) represent in a confidence interval?

A The percentage of intervals that will contain the true parameter if we repeat the experiment many times

B The probability that the true parameter is inside the calculated interval for this sample

C The percentage of data points inside the interval

D The chance that the sample mean equals the population mean

The confidence level means that if we repeat the sampling many times, that percentage of intervals will contain the true parameter.

Which R function can you use to get a confidence interval for a sample mean?

A mean()

B summary()

C t.test()

D confint()

t.test() calculates confidence intervals for the mean by default.

If a confidence interval for a mean is very narrow, what does it suggest?

A High uncertainty about the estimate

B The sample size is too small

C The data is biased

D Low variability or large sample size

A narrow interval usually means the estimate is precise due to low variability or a large sample.

What happens to the width of a confidence interval if you increase the confidence level from 95% to 99%?

A It becomes wider

B It stays the same

C It becomes narrower

D It becomes zero

Higher confidence levels require wider intervals to be more sure the true value is inside.

Which of these is NOT a reason for a wide confidence interval?

A Small sample size

B Large sample size

C High confidence level

D High data variability

A large sample size usually makes the interval narrower, not wider.

Explain what a confidence interval is and how you would calculate it in R for a sample mean.

Think about how sample data estimates a population value and how R helps with this.

Describe how the width of a confidence interval changes with sample size and confidence level.

Consider what makes us more or less sure about our estimate.