Confidence intervals in R Programming - Mini Project: Build & Apply

Confidence Intervals in R

📖 Scenario: You are a data analyst working with a small dataset of exam scores. You want to understand the range in which the true average score likely falls by calculating a confidence interval.

🎯 Goal: Build an R script that calculates a 95% confidence interval for the mean of a given numeric dataset.

📋 What You'll Learn

Create a numeric vector called scores with the exact values: 78, 85, 92, 88, 76, 95, 89

Create a variable called confidence_level and set it to 0.95

Calculate the 95% confidence interval for the mean of scores using the t.test() function and store the result in conf_interval

Print the confidence interval stored in conf_interval

💡 Why This Matters

🌍 Real World

Confidence intervals help us understand the range where the true average of a population likely lies based on sample data.

💼 Career

Data analysts and scientists use confidence intervals to make informed decisions and report uncertainty in their findings.

1

Create the data vector

Create a numeric vector called scores with these exact values: 78, 85, 92, 88, 76, 95, 89

R Programming

# Create the numeric vector scores with the given values
# Your code here

Hint

Use the c() function to combine numbers into a vector.

2

Set the confidence level

Create a variable called confidence_level and set it to 0.95

R Programming

scores <- c(78, 85, 92, 88, 76, 95, 89)
# Create the confidence_level variable and set it to 0.95
# Your code here

Hint

Just assign the number 0.95 to the variable confidence_level.

3

Calculate the confidence interval

Use the t.test() function with scores and conf.level = confidence_level to calculate the confidence interval. Store the result in a variable called conf_interval

R Programming

scores <- c(78, 85, 92, 88, 76, 95, 89)
confidence_level <- 0.95
# Calculate the confidence interval using t.test and store in conf_interval
# Your code here

Hint

Use t.test(scores, conf.level = confidence_level) to get the confidence interval.

4

Print the confidence interval

Print the confidence interval stored in conf_interval by accessing its conf.int element

R Programming

scores <- c(78, 85, 92, 88, 76, 95, 89)
confidence_level <- 0.95
conf_interval <- t.test(scores, conf.level = confidence_level)
# Print the confidence interval
# Your code here

Hint

Use print(conf_interval$conf.int) to show the confidence interval.

Practice

1. What does a 95% confidence interval represent in statistics?

easy

A. The percentage of data points within one standard deviation

B. The probability that the sample mean is exactly 95

C. The range of values that includes 95 data points

D. A range that likely contains the true population parameter 95% of the time

Solution

1. Step 1: Understand confidence interval meaning

   A confidence interval estimates a range where the true population parameter lies based on sample data.

2. Step 2: Interpret 95% confidence level

   A 95% confidence interval means if we repeat sampling many times, 95% of those intervals will contain the true parameter.

3. Final Answer:

   A range that likely contains the true population parameter 95% of the time -> Option D

4. Quick Check:

   Confidence interval = range with true value 95% [OK]

Hint: Confidence interval shows where true value likely lies [OK]

Common Mistakes:

• Confusing confidence interval with probability of sample mean
• Thinking it counts data points inside the interval
• Mixing confidence level with standard deviation coverage

2. Which R function is commonly used to calculate a confidence interval for a sample mean?

easy

A. confint()

B. mean()

C. t.test()

D. summary()

Solution

1. Step 1: Identify function for confidence intervals

   The t.test() function in R calculates confidence intervals for means using t-distribution.

2. Step 2: Compare with other functions

   confint() is for model objects, mean() calculates mean only, summary() gives summary stats but no CI.

3. Final Answer:

   t.test() -> Option C

4. Quick Check:

   Use t.test() for confidence intervals [OK]

Hint: Use t.test() to get confidence intervals in R [OK]

Common Mistakes:

• Using mean() expecting confidence intervals
• Confusing confint() with t.test()
• Assuming summary() returns confidence intervals

3. What is the output of this R code snippet?

set.seed(123)
sample_data <- rnorm(30, mean=50, sd=10)
test_result <- t.test(sample_data, conf.level=0.99)
test_result$conf.int

medium

A. [43.5, 56.5]

B. [42.9, 57.1]

C. [44.2, 55.8]

D. [45.0, 56.0]

Solution

1. Step 1: Generate sample and run t.test()

   The code generates 30 random normal values with mean 50 and sd 10, then calculates 99% confidence interval.

2. Step 2: Calculate 99% confidence interval

   Using t-distribution with 29 degrees of freedom, the interval is approximately [42.9, 57.1].

3. Final Answer:

   [42.9, 57.1] -> Option B

4. Quick Check:

   t.test() 99% CI ≈ [42.9, 57.1] [OK]

Hint: Remember t.test() returns conf.int vector [OK]

Common Mistakes:

• Using 95% CI instead of 99%
• Ignoring set.seed causing different results
• Misreading output bounds

4. Identify the error in this R code that tries to calculate a 90% confidence interval:

data <- c(5, 7, 8, 6, 9)
test <- t.test(data, conf.level=90)
test$conf.int

medium

A. conf.level should be between 0 and 1, not 90

B. t.test() cannot be used on numeric vectors

C. Missing parentheses in t.test call

D. conf.int is not a valid attribute of t.test output

Solution

1. Step 1: Check conf.level argument

   The conf.level argument expects a decimal between 0 and 1, e.g., 0.90 for 90% confidence.

2. Step 2: Identify incorrect usage

   Passing 90 instead of 0.90 causes an error because it's out of valid range.

3. Final Answer:

   conf.level should be between 0 and 1, not 90 -> Option A

4. Quick Check:

   conf.level = 0.90, not 90 [OK]

Hint: conf.level must be decimal like 0.90, not whole number [OK]

Common Mistakes:

• Using conf.level=90 instead of 0.90
• Thinking t.test() needs special input type
• Trying to access non-existent attributes

5. You have two independent samples:

group1 <- c(20, 22, 19, 24, 21)
group2 <- c(30, 28, 35, 32, 31)

How do you calculate a 95% confidence interval for the difference in means between these groups in R?

hard

A. t.test(group1, group2, conf.level=0.95, paired=FALSE)

B. t.test(group1, group2, conf.level=0.95, paired=TRUE)

C. mean(group1) - mean(group2)

D. confint(lm(group1 ~ group2))

Solution

1. Step 1: Identify test type for independent samples

   Since group1 and group2 are independent, use paired=FALSE in t.test().

2. Step 2: Use t.test() with correct parameters

   Call t.test(group1, group2, conf.level=0.95, paired=FALSE) to get the 95% confidence interval for difference in means.

3. Final Answer:

   t.test(group1, group2, conf.level=0.95, paired=FALSE) -> Option A

4. Quick Check:

   Independent samples use paired=FALSE [OK]

Hint: Use paired=FALSE for independent samples in t.test() [OK]

Common Mistakes:

• Using paired=TRUE for independent samples
• Calculating difference of means manually without CI
• Using confint() on lm() incorrectly