| Course | HS345 Biostatistics |
|---|---|
| Unit | Unit 5 |
| Paper type | Sampling distribution exercise |
| Length | About 560 words, 5 pages double-spaced |
| Format | APA 7 student paper |
| School | Purdue University Global |
| Program | BS in Health Science |
| Updated | October 2026 |
Free sample paper for HS345 Unit 5
A Year of Ambulance Calls as a Known Population: A Unit 5 Sampling Distribution Exercise With Samples of 4, 16 and 64
[Student Name]
Purdue University Global
HS345: Biostatistics
Unit 5 Sampling Distribution Exercise
[Instructor Name]
[Date]
The county, its call log and the simulated samples are composite; the statistics sources cited are real.
The Population
The call log holds [5,200] response times, measured from dispatch to arrival. Population mean: 9.37 minutes. Standard deviation: 4.82 minutes. Median: 8.59 minutes. Response times pile up between 5 and 12 minutes and then thin out slowly toward distant rural addresses, the slowest past 37 minutes; 12.3 percent of calls took longer than 15 minutes. The mean sits above the median because of that tail.
The Simulation
For each of three sample sizes, 4, 16 and 64 calls, the exercise drew 2,000 random samples from the log and recorded each sample's mean. That produced three sampling distributions, one per size, each shown as a histogram on the same horizontal scale as the population.
What the Sample Means Did
Center: at every size the average of the 2,000 sample means fell within a few hundredths of a minute of 9.37. The sample mean is an unbiased estimate of the population mean whatever the size.
Spread: the standard deviation of the sample means shrank as the sample grew.
Size 4: observed spread 2.30 minutes; predicted by the formula, 4.82 divided by the square root of 4, or 2.41. Size 16: observed 1.24; predicted 1.20. Size 64: observed 0.59; predicted 0.60.
The predicted value is the standard error of the mean, sigma over the square root of n (Altman & Bland, 2005). The observed and predicted spreads agree closely, and the small differences come from using 2,000 samples rather than every possible sample.
Quadrupling the sample size halved the spread of the sample means each time, which is the square root of n doing exactly what the formula says.
Shape: the population's skewness was about 1.0. The sample means at size 4 were still visibly skewed, at about 0.5; at size 16 about 0.25; and at size 64 the histogram looked close to a normal curve, skewness about 0.12. The central limit theorem predicts this: means of larger samples have distributions closer to normal even when the population is skewed (Pagano et al., 2022).
What It Means for a Manager
Suppose the service's director checks response times by pulling 16 random calls each month. Even if nothing changes, those monthly means will typically wander by about plus or minus 1.2 minutes from the true 9.4, and about one month in twenty will land more than 2.4 minutes away by chance. A director who reacts to every month above 10 minutes will be chasing noise. With 64 calls the wandering shrinks to about 0.6 minutes, which makes a real change of a minute much easier to see.
A Caution About the Tail
The mean response time describes the average call, but the people waiting longest are in the tail. A sample mean of 9 minutes is consistent with one call in eight taking over 15 minutes. For a service whose standard concerns the slowest calls, the share over a threshold, or a high percentile, is a better measure than the mean, and its sampling behavior should be studied separately (Bland, 2015).
References
Altman, D. G., & Bland, J. M. (2005). Standard deviations and standard errors. BMJ, 331(7521), 903. https://doi.org/10.1136/bmj.331.7521.903
Bland, M. (2015). An introduction to medical statistics (4th ed.). Oxford University Press.
Pagano, M., Gauvreau, K., & Mattie, H. (2022). Principles of biostatistics (3rd ed.). CRC Press.
What the HS345 Unit 5 assignment asks for
The fifth unit usually asks you to simulate or describe the sampling distribution of a mean, using an applet, software or a supplied dataset, and to connect what you see with the standard error and the central limit theorem. Two to three pages with figures is typical. Graders want the population described first, the sampling procedure stated clearly, the center, spread and shape of the sample means reported at each size, and a comparison with the formula. Interpretation for a real decision maker earns extra credit. Explain why simulated values differ slightly from theory. Cite a statistics source for the standard error and the theorem, and report any software or applet settings so the work could be repeated.
Inside the HS345 Unit 5 example
The exercise opens with the population's mean, standard deviation, median and tail. A short section explains the simulation, three sample sizes with 2,000 samples each. Results are given for center, spread and shape in turn. The spread section lists observed and predicted standard errors side by side; the highlighted sentence names the square-root rule they demonstrate. The shape section reports skewness falling as samples grow and ties it to the central limit theorem. A section for the service director translates the standard error into how far a monthly sample of sixteen calls will wander, and a closing caution recommends tracking the share of slow calls alongside the mean.
HS345 Unit 5 rubric: what earns full points
Marks in a sampling distribution exercise rest mainly on correctly describing the simulation results and connecting them to theory. Description credit requires center, spread and shape at each sample size, with numbers. Theory credit comes from comparing observed spread with the standard error formula and explaining the central limit theorem's role in the changing shape. Interpretation is rewarded when results are turned into practical guidance, such as how much variation to expect in routine monitoring. Reproducibility, meaning settings and procedures stated clearly, adds points. Tables that put observed and predicted values side by side make the comparison easy to grade. A figure with all four histograms on one horizontal scale makes the narrowing visible at a glance and is often what convinces a grader.
HS345 Unit 5 help from the desk
A common confusion is between the standard deviation of the population and the standard error of the mean, which shrinks with sample size while the population spread does not. Another is claiming the population itself becomes normal as samples grow. Some students report only the spread and forget center and shape. Others give simulation results with no comparison to the formula. Leaving out the number of repetitions makes the work impossible to check. If your course uses a different population or an online applet, share its settings and the sample sizes required, and the comparison with theory can be laid out the same way.
Get an HS345 Unit 5 example written to your instructions
Your HS345 Unit 5 exercise may supply a population, a simulation applet or only parameters, and a custom sample works from whichever it provides. Forward the prompt with the rubric and any file. Returned in 24-48 hours at no charge the first time, the sample keeps population, sample and sampling distribution visibly separate and checks every standard error against the data. The paper above is an original model document written by our desk, not a submitted student paper and not an official Purdue University Global document.
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HS345 Unit 5 questions, answered
Why do the simulated spreads not match the formula exactly?
Because 2,000 samples is a large but finite number, so the simulated standard deviation of the means carries its own sampling error. At n of 4 the skewed population adds a small further gap. The example reports both figures and explains that close agreement, not perfect agreement, is what a simulation is expected to show.
Is it realistic to know a population mean?
Occasionally. A full year of dispatch records, every discharge in a hospital's database or a complete registry can be treated as a population for a defined question. Most research samples because the population is unavailable. The exercise uses a known population so that the behavior of sample means can be checked against a true value rather than assumed.
What if my course uses an applet instead of a dataset?
The same structure works. Report the population settings the applet uses, the sample sizes chosen, the number of repetitions and the resulting spread and shape of the means. A custom sample can be built around the applet your section names, with screenshots described in words where the rubric asks for them.
Where can I find a free HS345 Unit 5 sample paper?
This page contains the whole Unit 5 exercise, following sample means of ambulance response times at sizes 4, 16 and 64.
How is the standard error different from the standard deviation?
One measures the scatter of single calls around 9.4 minutes; the other measures how far averages of many calls stray from it, and only that second figure narrows as samples get bigger.