| Course | HS345 Biostatistics |
|---|---|
| Unit | Unit 6 |
| Paper type | Confidence interval problem |
| Length | About 550 words, 4 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 6
A Range Over 600 Milligrams Wide: A Unit 6 Confidence Interval Problem on Sodium Intake at a Workplace Health Screening
[Student Name]
Purdue University Global
HS345: Biostatistics
Unit 6 Confidence Interval Problem
[Instructor Name]
[Date]
The company, its employees and their recalls are composite; the dietary guideline and the statistics sources cited are real.
Part A: The Inputs
Sample size: 36 employees. Sample mean: 3,180 milligrams of sodium per day. Sample standard deviation: 920 milligrams. Standard error: 920 over 6, since 6 is the square root of the sample size, giving 153.3 milligrams. Critical value: t on 35 degrees of freedom for 95 percent confidence, 2.030.
The t distribution is used rather than the normal because the spread of sodium intake across the whole workforce is not known and has to be estimated from these 36 recalls (Pagano et al., 2022).
Part B: The 95 Percent Interval
Margin of error: 2.030 times 153.3, or 311.3 milligrams. Interval: 3,180 minus 311.3 to 3,180 plus 311.3, or 2,869 to 3,491 milligrams.
Interpretation: if the screening were repeated many times with new random samples of 36 employees, about 95 percent of intervals built this way would contain the true mean intake of the company's workforce. This interval is one of them; it either contains the true mean or it does not.
The Dietary Guidelines for Americans advise adults to keep sodium under 2,300 milligrams a day (U.S. Department of Agriculture & U.S. Department of Health and Human Services, 2020). The entire interval lies above that limit.
The interval is wide, but every value in it is at least 569 milligrams above the recommended limit, so its width does not weaken the one conclusion the committee needs.
Part C: The Price of More Confidence
At 90 percent: t on 35 degrees of freedom is 1.690. Margin 259.1; interval 2,921 to 3,439; width about 518 milligrams. At 99 percent: t is 2.724. Margin 417.6; interval 2,762 to 3,598; width about 835 milligrams.
More confidence costs width. Moving from 90 to 99 percent confidence widened the interval by about 60 percent, with the same data.
Part D: How Many Employees Next Time?
The committee wants a future estimate within plus or minus 150 milligrams at 95 percent confidence. Using the current standard deviation as a planning value and the normal approximation, n equals 1.96 times 920 divided by 150, squared: 12.02 squared, or about 145 employees. Recruiting 160 would allow for incomplete recalls.
Limits of the Conclusion
The wellness group may reasonably infer that average sodium intake among employees like these is very likely well above the recommended limit. It cannot conclude much about individuals, since a single day's recall varies widely from day to day, and the standard deviation of 920 reflects that day-to-day variation as much as differences between people. It also cannot generalize beyond employees who volunteered for the screening, who may eat differently from those who did not (Bland, 2015). A practical next step is a change to the company cafeteria's lower-sodium options, with the screening repeated in a year using a larger sample. If the company also wants to track change, the second screening should use the same recall method and season, since sodium intake shifts with holiday eating and summer menus.
References
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.
U.S. Department of Agriculture & U.S. Department of Health and Human Services. (2020). Dietary guidelines for Americans, 2020-2025 (9th ed.). https://www.dietaryguidelines.gov
HS345 Unit 6 instructions, in plain terms
Unit 6 typically gives a sample mean, standard deviation and size, and asks for a confidence interval, its interpretation, comparison with a benchmark and often a sample size calculation. Solutions usually fit in two or three pages. Credit goes to a correct standard error, the right critical value, a correctly built interval and an interpretation that describes the population mean rather than individuals. Many sections also ask how the interval changes with confidence level and how large a sample would achieve a given margin. Show every input and step. Name your sources: a textbook for the interval method, and the guideline or standard that supplies the benchmark.
How this HS345 Unit 6 example is built
Part A lists the inputs, computes the standard error and explains why a t value is used. Part B builds the 95 percent interval, interprets it in terms of repeated sampling and sets it against the dietary guideline; the highlighted sentence explains why the interval's width does not weaken the main conclusion. Part C repeats the calculation at 90 and 99 percent and shows how much width extra confidence costs. Part D works out the sample needed for a margin of 150 milligrams and adds an allowance for incomplete recalls. A closing section states what the wellness group may and may not infer, including day-to-day variation and volunteer bias, and suggests a cafeteria change with a repeat screening.
Where the points sit in the HS345 Unit 6 rubric
Confidence interval problems are graded mainly on correct construction and correct interpretation. Construction covers the standard error, critical value and arithmetic, with partial credit when steps are visible. Interpretation earns the most when it describes the population mean and avoids saying that 95 percent of individuals fall in the range. Comparison with a benchmark is rewarded when the conclusion follows from where the interval sits. Sample size work earns points for correct formula use and a sensible allowance for loss. Clear labeling of units, and a short discussion of limits such as volunteer samples, round out a strong solution. Writing the interpretation in a single plain sentence before any caveats shows the grader you know what the interval estimates.
HS345 Unit 6 help from the desk
The most common misreading is that the interval contains 95 percent of the employees' intakes. Another is using 1.96 when the standard deviation came from the sample and the sample is small. Some students compute the interval correctly but never compare it with the benchmark the problem provides. Others forget that a one-day recall varies widely within a person. Sample size answers that are not rounded up fall short of the target margin. If your problem involves a proportion or a different measure, share the numbers and the benchmark, and the interval can be built and read in the same order.
Get an HS345 Unit 6 example written to your instructions
Share the numbers your HS345 Unit 6 problem gives, whether a mean, a proportion or raw data, together with its instructions and rubric. A free first custom sample, ready in 24-48 hours, builds the interval with the right critical value, words the interpretation the way graders credit, and explains what the range's width allows anyone to conclude. 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 6 questions, answered
Why a t value instead of 1.96?
Because the standard deviation of 920 comes from the sample, not from a known population. The t distribution widens the interval slightly to account for that extra uncertainty, and with 35 degrees of freedom its critical value is 2.030. The difference from 1.96 is modest at this sample size but grows quickly in smaller samples.
Does the interval mean 95 percent of employees eat between 2,869 and 3,491 milligrams?
No, and that misreading is common. The interval describes the average intake of the workforce, not individuals. Individual intakes vary far more, as the standard deviation of 920 shows. A range covering most individuals would be a different calculation entirely, and the example flags the difference in a sentence near the end.
What if my problem gives a proportion instead of a mean?
The structure stays the same: inputs, standard error, critical value, interval, interpretation and comparison with a benchmark. The standard error formula changes to one based on the sample proportion, and the course may ask for a check that successes and failures are both large enough. A custom sample follows whichever form your prompt uses.
Where can I find a free HS345 Unit 6 sample paper?
You can read the complete Unit 6 problem here, building a confidence interval for employee sodium intake and comparing it with the dietary limit.
How do you choose a sample size for a confidence interval?
Decide the margin of error you need, use a planning value for the standard deviation, and solve for n with the critical value, rounding up and adding a margin for incomplete data.