Best examples of confidence intervals lab report examples for statistics labs

Examples of confidence intervals lab report examples in real student reports

Before talking theory, let’s start with how this actually looks in a lab report. These examples of confidence intervals lab report examples are written in the kind of language instructors expect: full sentences, clear context, and interpretation in plain English.

Example 1: Mean systolic blood pressure in a campus sample

Scenario
You measure systolic blood pressure for 40 students and want a 95% confidence interval for the population mean.

Sample results

• Sample mean (\(\bar{x}\)) = 118.6 mmHg
• Sample standard deviation (s) = 12.3 mmHg
• n = 40
• Confidence level: 95%, using a t-interval

Lab report wording (results section)

We estimated the average systolic blood pressure among students at our university using a 95% confidence interval. The sample of 40 students had a mean of 118.6 mmHg (SD = 12.3). Assuming approximately normal blood pressure in the population, the 95% confidence interval for the population mean was (114.7, 122.5) mmHg.

Interpretation sentence

We are 95% confident that the true mean systolic blood pressure for students at this university lies between 114.7 and 122.5 mmHg.

This is one of the best examples to copy structurally: context first, then numbers, then the interval, then a single, clear interpretation.

For background on why we use t-distributions for means with smaller samples, check out the introductory materials on confidence intervals from Khan Academy and the conceptual overview from UCLA’s IDRE.

Example 2: Proportion of vaccinated students (one-sample proportion CI)

Scenario
A public health lab asks: What proportion of students received the current season’s flu vaccine?

Sample results

• n = 200 students
• x = 96 report being vaccinated
• Sample proportion (\(\hat{p}\)) = 0.48
• 95% confidence interval using a normal approximation

Lab report wording

We estimated the proportion of students who received the 2024–2025 seasonal influenza vaccine. Out of 200 surveyed students, 96 reported being vaccinated (\(\hat{p} = 0.48\)). The 95% confidence interval for the true vaccination proportion was (0.41, 0.55).

Interpretation

Based on this sample, we are 95% confident that between 41% and 55% of students at this university were vaccinated against influenza in the 2024–2025 season.

If you want to connect your report to real-world data, the CDC maintains current vaccination statistics at CDC Flu Vaccination Coverage.

Example 3: Difference in mean sleep hours between athletes and non‑athletes

This is a classic two-sample confidence interval and one of the most common examples of confidence intervals lab report examples you’ll see in intro statistics.

Scenario
You compare average nightly sleep for student athletes vs. non‑athletes.

Sample results

• Athletes: n = 30, mean = 7.2 hours, SD = 0.9
• Non‑athletes: n = 35, mean = 6.6 hours, SD = 1.1
• 95% CI for \(\mu_\text{athletes} - \mu_\text{nonathletes}\)

Lab report wording

We compared average sleep duration between student athletes and non‑athletes using a two-sample t confidence interval. Athletes (n = 30) slept an average of 7.2 hours per night (SD = 0.9), whereas non‑athletes (n = 35) slept an average of 6.6 hours (SD = 1.1). The 95% confidence interval for the difference in population means (athletes − non‑athletes) was (0.1, 1.1) hours.

Interpretation

Because the entire interval is above 0, the data are consistent with athletes sleeping, on average, between 0.1 and 1.1 hours more per night than non‑athletes.

This example of a confidence interval shows how you can directly connect the sign of the interval to a practical conclusion.

Example 4: Proportion difference in mask use (two-sample proportion CI)

Scenario
You survey mask use in two campus locations.

Sample results

• Library: n = 120, masked = 78 → \(\hat{p}_1 = 0.65\)
• Dining hall: n = 150, masked = 60 → \(\hat{p}_2 = 0.40\)
• 95% CI for \(p_1 - p_2\)

Lab report wording

We estimated the difference in mask use between students observed in the library and those in the dining hall. In the library, 78 of 120 students wore masks (\(\hat{p}_1 = 0.65\)), while in the dining hall, 60 of 150 students wore masks (\(\hat{p}_2 = 0.40\)). The 95% confidence interval for the difference in population proportions (library − dining hall) was (0.15, 0.35).

Interpretation

We are 95% confident that the true proportion of students wearing masks is between 15 and 35 percentage points higher in the library than in the dining hall.

Public health labs often compare proportions this way; the CDC’s COVID-19 data tracker uses similar logic when presenting confidence ranges for survey-based estimates.

Example 5: Confidence interval for a regression slope (study time vs. exam score)

Many students struggle to write about regression intervals, so this is one of the best examples of confidence intervals lab report examples to keep handy.

Scenario
You run a simple linear regression predicting exam score from hours studied.

Regression output (simplified)

• Slope estimate (\(\hat{\beta}_1\)) = 4.3 points per hour
• Standard error of slope = 1.1
• 95% CI for slope = (2.1, 6.5)

Lab report wording

We modeled exam score as a function of hours studied using simple linear regression. The estimated slope was 4.3 (SE = 1.1), meaning each additional hour of study was associated with an increase of 4.3 points in exam score. The 95% confidence interval for the slope was (2.1, 6.5) points per hour.

Interpretation

We are 95% confident that each additional hour of studying is associated with an increase of between 2.1 and 6.5 exam points, on average, among students similar to those in our sample.

This example of a confidence interval highlights that regression intervals are about the parameter (slope), not individual predictions.

Example 6: Quality control for lightbulb lifetime (mean with known \(\sigma\))

Scenario
A manufacturer tests 50 LED bulbs from a production batch.

Sample results

• n = 50
• Mean lifetime = 24,800 hours
• Population \(\sigma\) assumed known from long-run data = 1,500 hours
• 99% confidence interval using a z-interval

Lab report wording

To evaluate the average lifetime of LED bulbs from the current production batch, we computed a 99% confidence interval assuming a known population standard deviation of 1,500 hours based on historical quality-control data. For 50 bulbs, the mean observed lifetime was 24,800 hours. The resulting 99% confidence interval for the population mean lifetime was (24,246, 25,354) hours.

Interpretation

We are 99% confident that the true mean lifetime of bulbs from this batch lies between 24,246 and 25,354 hours, which meets the company’s advertised target of 24,000 hours.

This kind of example of confidence intervals shows up in engineering and manufacturing labs.

Example 7: Medical trial – confidence interval for risk ratio

Scenario
A small randomized trial compares a new treatment vs. standard care for a binary outcome (improvement vs. no improvement).

Sample results

• New treatment: 60/80 improved (\(\hat{p}_1 = 0.75\))
• Standard care: 44/80 improved (\(\hat{p}_2 = 0.55\))
• Estimated risk ratio = 0.75 / 0.55 ≈ 1.36
• 95% CI for risk ratio = (1.03, 1.79)

Lab report wording

In the clinical trial, 75% of participants receiving the new treatment improved, compared with 55% under standard care. The estimated risk ratio for improvement was 1.36, with a 95% confidence interval of (1.03, 1.79).

Interpretation

We are 95% confident that the true improvement rate under the new treatment is between 3% and 79% higher than under standard care. Because the interval does not include 1, the data are consistent with a real treatment benefit.

For more on interpreting risk ratios and their intervals, see the introductory materials from the National Library of Medicine and clinical statistics tutorials from Harvard T.H. Chan School of Public Health.

How to write your own examples of confidence intervals lab report examples

Having seen several real examples of confidence intervals lab report examples, the pattern should feel familiar. Good write‑ups usually follow this structure in prose:

• State the research question in plain language.
• Describe the sample and statistic (mean, proportion, difference, slope).
• Name the type of interval (one-sample mean, two-sample proportion, etc.).
• Report the confidence level and the interval itself.
• Interpret the interval in context, in one or two sentences.

Here’s a template you can adapt:

We estimated [parameter] for [population] using a [confidence level]% confidence interval based on [sample description]. The sample [statistic] was [value]. The [confidence level]% confidence interval for the [parameter] was ([lower bound], [upper bound]). We are [confidence level]% confident that [parameter in words] lies between [lower bound] and [upper bound] for [population].

You can plug almost any of the examples of confidence intervals lab report examples above into this template and they will still read naturally.

Common mistakes seen in confidence interval lab report examples

When instructors grade, they tend to see the same errors over and over. If you want your work to stand out from other examples of confidence intervals lab report examples, avoid these pitfalls:

Misinterpreting confidence level

Students often write that “95% of the data fall inside the interval” or “there is a 95% chance the true mean is in this interval.” Both are off.

Better wording:

We are 95% confident that the interval from A to B captures the true population mean.

The confidence is about the method in repeated sampling, not about a probability attached to a fixed parameter.

Ignoring direction for differences

For differences in means or proportions, always specify the order. In the earlier sleep example of confidence intervals, the parameter was defined as \(\mu_\text{athletes} - \mu_\text{nonathletes}\). That definition makes it easy to interpret an interval like (0.1, 1.1) as “athletes sleep more.”

Reporting too many decimal places

Most instructors prefer intervals rounded to two decimal places (or to one for hours, years, or simple scores). Over‑precision makes your report harder to read without adding information.

Dropping context

An interval like (3.2, 5.8) means nothing without units and population. Always specify what the numbers refer to: hours of sleep per night for undergraduates at your university, or percentage of vaccinated adults in a given city.

Using real data to strengthen your confidence interval examples

If your instructor allows it, connecting your lab to real-world statistics makes your work more convincing and more fun to read. For instance:

• When writing about blood pressure or cholesterol, you can compare your confidence interval to reference ranges from NIH’s MedlinePlus.
• For public health or epidemiology labs, you can compare your estimated proportions to national data from CDC.
• For educational or psychological variables, many labs mirror classic studies summarized on university sites like Harvard or other .edu resources.

You might write something like:

Our 95% confidence interval for mean systolic blood pressure among students (114.7 to 122.5 mmHg) is lower than typical adult reference levels reported by the NIH, which often cite 120 mmHg as the upper bound for normal.

That kind of sentence shows you can interpret intervals in a broader context, which is what instructors want to see in the best examples of confidence intervals lab report examples.

FAQ: examples of confidence intervals in lab reports

Q: Can you show a short example of a confidence interval sentence I can reuse?
Yes. Here is a compact example of a confidence interval statement:

The sample mean exam score was 78.4 (SD = 9.2, n = 45). The 95% confidence interval for the population mean exam score was (75.7, 81.1). We are 95% confident that the true mean exam score for students in this course lies between 75.7 and 81.1.

You can adjust the variable, units, and numbers to match your own data.

Q: How many decimal places should I use in examples of confidence intervals lab report examples?
Generally, two decimal places are enough for most intervals, and sometimes one is better for units like hours or years. The key is consistency: use the same level of rounding for both bounds of the interval and for related statistics.

Q: Do I always need to show the formula in my lab report, or are written examples enough?
This depends on your instructor. Many lab guidelines ask for both: a brief formula (for example, \(\bar{x} \pm t^* \cdot s/\sqrt{n}\)) and a written interpretation. The written examples of confidence intervals lab report examples above are usually sufficient for the results section, while formulas often go in the methods or appendix.

Q: How do I explain when a confidence interval includes 0 or 1?
For differences in means or proportions, an interval that includes 0 suggests the data are consistent with no difference between groups. For ratios (risk ratios, odds ratios), an interval that includes 1 suggests no difference in risk. In your lab report, you might say:

Because the 95% confidence interval for the difference in means (−0.3, 1.2) includes 0, the data do not provide strong evidence of a difference in average sleep duration between the two groups.

Q: Where can I find more real examples of confidence intervals in published research?
Look at the results sections of articles in medical and social science journals. Many are indexed on PubMed. Search for terms like “95% confidence interval” and skim how authors phrase their intervals. That will give you high‑quality, real examples of confidence intervals lab report examples to model your own writing after.