STA 2010 Module 4 Sample Paper

Comparing Order Picking Times Under Two Aisle Layouts at a Regional Distribution Center

Student Name

Thomas Edison State University

STA-2010: Principles of Statistics

Module 4 Written Assignment

Mentor Name

April 14, 2026

What this page is doingThe title names the comparison, the measure and the setting, so a reader knows the paper's job before the first paragraph. A statistics write up titled Hypothesis Testing tells a rubric nothing. Naming the two layouts and the outcome variable also commits the writer to a single testable question, which is what stops the paper drifting into a general essay about t tests. The course line carries the hyphenated code form the school uses, and the module line uses the query wording rather than an invented deliverable name.

The Operating Question and the Data

Northbay Distribution is a composite regional fulfillment center that ships replenishment orders to 84 retail outlets across three states. The center picks from eight aisles. In January the operations group retrofitted a single aisle, Aisle B, with a revised pick path that reorders bin faces by movement velocity and shortens the walk between the two heaviest bin groups. The remaining seven aisles kept the original layout. Retrofitting all seven would cost about $61,000 in racking, labeling and downtime, and the operations manager has asked whether the recorded pick times justify that spend. The measured variable is pick cycle time in minutes, taken from scan in at the aisle head to tote release at the conveyor.

The data set is a random sample drawn from the warehouse execution system's cycle log for a single 30 day period, March 2 through March 31. Cycle identifiers for the period were listed separately for each aisle and a random number generator selected 38 records from Aisle A and 41 from Aisle B. Only single tote cycles were eligible, so that a long cycle covering three totes could not be compared against a short cycle covering one. Cycles flagged by the system as interrupted by an equipment fault were removed before sampling rather than after, so the exclusion rule could not be influenced by the times themselves. No operator is identified in the extract.

Aisle A produced a mean cycle time of 14.8 minutes with a standard deviation of 3.42 minutes across 38 cycles. Aisle B produced a mean of 13.1 minutes with a standard deviation of 3.06 minutes across 41 cycles. The medians sit close to the means, 14.6 and 12.9 minutes, and both distributions show a mild right tail of the kind that time data usually shows, with the largest single value at 22.4 minutes. The ratio of the larger variance to the smaller is 1.25. The observed difference of 1.7 minutes is the entire question, and everything that follows asks whether a gap that size is a reasonable thing to see when two layouts perform identically.

What this page is doingNotice that the sampling rule appears before any figure. Saying how the 79 cycles were selected, and that fault interrupted cycles were removed before rather than after sampling, is what separates a defensible analysis from one that quietly chose its own result. The descriptive block then gives the reader everything needed to check the arithmetic later: two means, two standard deviations, two sample sizes, and the variance ratio. Rubrics for a first inference module almost always look for the data description before the test, and this ordering earns that point without a sentence of filler.

Hypotheses, Assumptions, and Choice of Test

The null hypothesis is that the population mean cycle time is the same under both layouts, so that the difference between them is zero. The alternative is that the two population means differ, stated without a direction. A two sided alternative is the honest choice here even though the operations group expects an improvement, because a retrofit that slowed picking would be at least as important to detect as one that sped it up, and a one sided test would leave that outcome invisible. The significance level was fixed at .05 before the sample was drawn, and the decision rule was written down at the same time so that it could not be adjusted once the numbers were in view.

Three assumptions carry the test. Independence holds by construction: each sampled cycle is a separate order handled once, the two aisles draw from separate operator rosters on the sampled shifts, and no cycle appears in both groups. Approximate normality of the sampling distribution is supportable at these sample sizes; both groups exceed 30 observations, the histograms are unimodal with a mild right tail, and the largest observation sits about 2.2 standard deviations above its own group mean rather than far outside the body of the data. The response is measured on a continuous scale in minutes to one decimal place. Nothing in the extract suggests a rounding floor or a system timeout that would truncate long cycles.

An independent samples t test fits the design, since the two groups contain different cycles and there is no meaningful pairing between a cycle in Aisle A and a cycle in Aisle B. Welch's version is used rather than the pooled version. The variance ratio of 1.25 is modest and a pooled test would probably behave acceptably, but Welch's test is used here as the default rather than as a fallback, because it holds its stated error rate when variances differ and costs almost nothing when they do not (Delacre et al., 2017). Choosing the test from the design rather than from the outcome of a preliminary variance test also keeps the reported error rate honest.

What this page is doingTwo moves here are worth copying. The first is stating why the alternative is two sided instead of asserting it, which shows the reasoning a rubric row on hypothesis formulation is written to find. The second is checking assumptions against the actual data, naming the sample sizes, the shape of the histograms and the position of the largest value, rather than reciting the assumption list from the text. Justifying Welch by design rather than by a preliminary variance test is the kind of detail that separates a competent write up from a mechanical one.

Results

The standard error of the difference is the square root of 3.42 squared divided by 38 plus 3.06 squared divided by 41, which gives 0.73 minutes. The difference in sample means, 1.7 minutes, divided by that standard error gives t = 2.32. The Welch approximation puts the degrees of freedom at 74.39 rather than at the 77 a pooled test would use. Against a two sided critical value of 1.99 at the .05 level, the obtained statistic falls in the rejection region, and the exact two sided p value is .023. The null hypothesis of equal mean cycle times is rejected: t(74.39) = 2.32, p = .023.

A decision alone is thin reporting, so the interval and the effect size follow. The 95 percent confidence interval for the difference in population means runs from 0.24 to 3.16 minutes, obtained by adding and subtracting 1.99 standard errors around the observed 1.7 minute gap. Cohen's d, computed against a pooled standard deviation of 3.24 minutes, is 0.53, a moderate standardized difference. The interval is wide relative to its own midpoint, which is the plain consequence of two samples of about 40 cycles each and a standard deviation near a quarter of the mean. A larger sample would narrow it without changing the estimate much.

The p value of .023 carries a narrow meaning that is easy to overstate. It is the probability of seeing a difference at least as large as 1.7 minutes in samples of this size if the two layouts truly produced the same mean cycle time; it is not the probability that the retrofit works, and it is not a measure of how large the improvement is (Wasserstein & Lazar, 2016). The interval, not the p value, is the number the manager should carry into the spending conversation, because it states the range of savings the data can support rather than only whether zero can be ruled out (Cumming, 2014).

What this page is doingThe results section reports the statistic in APA form, t(74.39) = 2.32, p = .023, and then refuses to stop there. Adding the confidence interval and Cohen's d answers the question a bare p value cannot: how much faster, and how sure are we about the size. The closing paragraph states what the p value means in one sentence and what it does not mean in the next, which is where most write ups lose marks by claiming the probability that the alternative is true.

What the Result Means for the Decision

The seven unmodified aisles together complete about 480 single tote cycles on an average operating day, and the center runs about 250 operating days a year. At the point estimate of 1.7 minutes saved per cycle, the retrofit returns 816 minutes a day, or 13.6 labor hours, which at a fully loaded picking rate of $27 an hour is roughly $367 a day and $91,800 a year against a one time cost of $61,000. That is a payback of about eight months. At the lower bound of the interval, 0.24 minutes, the same arithmetic returns 1.9 hours a day and about $12,960 a year, and the payback stretches to nearly five years.

That spread is the argument for a staged decision rather than a single approval. A result that is statistically significant at the level chosen is not automatically a result worth $61,000, and the lower bound of the interval is where that second question gets answered. The recommendation is to retrofit two aisles now at roughly $17,000, then draw a fresh sample of about 120 cycles per group and re estimate, which would cut the interval width by close to half. Two limits should travel with the recommendation: operators were not randomly assigned to aisles, so an experience difference could be doing part of the work, and a single 30 day window in March may not represent peak volume.

What this page is doingThis is the sheet that turns a class exercise into a piece of work someone would act on. The minutes are converted into hours, dollars and a payback period, and the same arithmetic is run twice, once at the point estimate and once at the lower bound of the interval, so the reader sees the range of futures the data allows. The two named limits, non random operator assignment and a single sampling window, are stated as limits on the recommendation rather than buried in a hedge.

References

American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). https://doi.org/10.1037/0000165-000

Cumming, G. (2014). The new statistics: Why and how. Psychological Science, 25(1), 7-29. https://doi.org/10.1177/0956797613504966

Delacre, M., Lakens, D., & Leys, C. (2017). Why psychologists should by default use Welch's t-test instead of Student's t-test. International Review of Social Psychology, 30(1), 92-101. https://doi.org/10.5334/irsp.82

Moore, D. S., Notz, W. I., & Fligner, M. A. (2021). The basic practice of statistics (9th ed.). W. H. Freeman.

Wasserstein, R. L., & Lazar, N. A. (2016). The ASA statement on p-values: Context, process, and purpose. The American Statistician, 70(2), 129-133. https://doi.org/10.1080/00031305.2016.1154108

How this STA 2010 Module 4 example is structured

Thomas Edison State University publishes no module by module deliverable names, so this STA 2010 Module 4 example follows the genre the module almost certainly wants at the undergraduate level: in many sections this module asks for a short written assignment that runs one inferential test on a described data set and explains the result, and your course instructions and rubric decide the exact form. The paper moves in four sections. The first states the scenario, the sample and the descriptive figures, because a reader cannot judge a test without the data behind it. The second sets the hypotheses and checks the assumptions before any test is named. The third reports the statistic, degrees of freedom, p value, interval and effect size in one place. The fourth converts the interval into the decision the operations manager actually faces.

STA-2010 Module 4 questions, answered

What does STA 2010 Module 4 usually ask for?

Thomas Edison State University does not publish a module by module deliverable list, so the form varies by section. In many sections this module asks for a short written assignment that runs one inferential test on a described data set and interprets the result in context. Your course instructions and rubric decide the exact form, including length and citation expectations.

Do I have to report a confidence interval and an effect size, or is the p value enough?

Report all three whenever the test compares means. The p value only says whether the observed gap is surprising under the null hypothesis. The interval says how large the difference plausibly is, and the effect size puts it on a standard scale so it can be compared across studies. APA 7 reporting conventions expect the interval alongside the test statistic.

Should I use Welch's t test or the pooled t test?

Use Welch by default for two independent groups. It does not require equal population variances, and when the variances are in fact equal it loses almost no power compared with the pooled test. Selecting the test after running a preliminary equality of variance check distorts the error rate, so choose from the design of the study, not from the sample.

Write yours, or have the desk draft it

This paper is an original model document written by our desk, not a submitted student paper and not an official Thomas Edison State University document. Read it for the moves, then write your own to the instructions in your classroom. If you want one built to your exact prompt and rubric, the first custom sample is free and arrives in 24 to 48 hours.

STA 2010 Module 4: sample paper, in real form