| Course | BU 321 Business Statistics |
|---|---|
| Unit | Unit 6 |
| Paper type | Two sample comparison paper |
| Length | About 1,040 words, 6 pages |
| Format | APA 7 student paper |
| School | Herzing University |
| Program | BS in Business Management |
| Updated | September 2026 |
Free sample paper for BU 321 Unit 6
Is Eastgate Really Slower Than Northside? A Two-Sample Comparison of Delivery Times at a Composite Pizza Chain, With the Difference Read as an Interval
Student Name
Business, Herzing University
BU 321: Business Statistics
Instructor Name
April 1, 2026
Is Eastgate Really Slower Than Northside? A Two-Sample Comparison of Delivery Times at a Composite Pizza Chain, With the Difference Read as an Interval
The Comparison a Manager Wants
Brickoven Express's area manager believes that the Eastgate store, one of the six stores in this composite Columbus pizza chain, delivers more slowly than the Northside store, and she is considering moving a driver from Northside to Eastgate on weeknights. Moving a driver costs Northside capacity, so she wants evidence that the difference is real before acting. This paper compares the two stores' delivery times from the October 2025 sample of 240 orders, 40 from each store. It summarizes both groups side by side, argues for the choice of test, checks conditions for each sample, runs the test with its working shown, reports the difference as an interval and reads the result back as a decision.
The Two Groups, Side by Side
Before any test, the table shows the difference the test will judge. Eastgate's sample mean is 2.25 minutes higher than Northside's, but Northside's delivery times vary more. The two stores' average delivery distances are almost the same, 3.10 miles at Eastgate and 3.25 miles at Northside, so a difference in times is not simply a difference in how far drivers travel.
| Measure | Eastgate | Northside |
|---|---|---|
| Orders sampled (n) | 40 | 40 |
| Mean delivery time (minutes) | 28.05 | 25.80 |
| Standard deviation (minutes) | 6.23 | 9.10 |
| Orders over 35 minutes | 6 (15.0%) | 5 (12.5%) |
| Mean distance (miles) | 3.10 | 3.25 |
Choosing the Test
Two decisions determine the test. The first is what was measured. Delivery time is a continuous measurement, so a comparison of means uses the full information in each observation. A comparison of proportions, such as the share of orders over 35 minutes, would discard most of that information, and with only 6 and 5 late orders the counts are too small for the normal approximation that a two-proportion test relies on, which usually requires at least 10 in each category (Anderson et al., 2020). A test of means is the better choice.
The second decision is whether the samples are independent or paired. Paired samples arise when each observation in one group is matched with a specific observation in the other, such as the same route timed before and after a change. Here the orders at Eastgate and Northside are different orders, from different customers, drawn separately, so the samples are independent. The standard deviations differ noticeably, 6.23 against 9.10, so the paper uses Welch's version of the two-sample t test, which does not assume equal population variances (Welch, 1947).
The pooled two-sample t test, which averages the two variances into one, was considered and set aside. It gives a slightly smaller standard error when the population variances really are equal, but when they differ, and especially when a manager cannot be sure, it can overstate the evidence. With a standard deviation nearly 50 percent larger at Northside, the safer choice is the version that lets each store keep its own variance, at the cost of a few degrees of freedom.
Checking Conditions for Each Sample
Each sample was drawn at random from its store's records, and 40 orders are a small fraction of each store's two-week deliveries, so observations within each sample are independent. Each sample has 40 observations; neither shows extreme outliers relative to its spread, and the pooled sample's skewness of 0.48 is modest. With samples of 40, the sampling distribution of each mean is approximately normal, which is sufficient for the t procedure (National Institute of Standards and Technology, 2012).
The Test
The hypotheses concern the difference between the two population means, Eastgate minus Northside. The null hypothesis is that the difference is zero; the alternative is that it is not zero. A two-tailed test is used because the area manager's decision would change if either store were clearly slower, and the significance level is 0.05, set before the calculation.
Combining the two sample variances, 6.23 squared over 40 plus 9.10 squared over 40, then square-rooting the total, yields a standard error for the difference of 1.744 minutes. The test statistic is t = 2.25 divided by 1.744 = 1.29. Welch's formula gives about 69 degrees of freedom. The two-tailed p-value is 0.20 (in Excel, T.TEST with type 3 on the two columns). Because 0.20 is greater than 0.05, the null hypothesis is not rejected.
An interval at 95 percent confidence around the difference uses a t critical value of about 1.995 with 69 degrees of freedom: 2.25 plus or minus 1.995 times 1.744 gives an interval from minus 1.23 to 5.73 minutes.
Reading the Difference Back as a Decision
The test does not show that Eastgate is slower. It also does not show that the stores are equally fast. The interval explains why. The data are consistent with Eastgate being about a minute faster than Northside and equally consistent with Eastgate being almost six minutes slower. A six-minute difference would matter a great deal to customers; a one-minute difference in either direction would not. With 40 orders from each store, the sample cannot tell these possibilities apart.
The standardized size of the observed difference, 2.25 minutes divided by the pooled standard deviation of about 7.8 minutes, is about 0.29, which Cohen (1988) would classify as a small effect. Even if the difference is real, it is modest compared with the variation among orders within each store.
For the area manager, the decision this supports is to hold off on moving a driver. The evidence is not strong enough to justify reducing Northside's capacity, and the difference, if it exists, is small compared with the order-to-order variation that more drivers would not remove. A better next step is to collect a larger sample, about 150 orders per store, which would narrow the interval to roughly plus or minus 1.8 minutes, and to look at when Eastgate's slow orders occur; the regression in Unit 7 shows that distance and time of day explain much of the variation in delivery times. All orders, stores and managers in this paper are fictional.
The next sample should also record the hour each order was placed and whether it came during a road closure or a driver shortage, since those details would let the chain separate a store effect from the conditions each store faced during the two weeks sampled. A difference that disappears once dinner-hour volume is taken into account would call for a scheduling change, not a driver transfer.
References
Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Cochran, J. J. (2020). Statistics for business and economics (14th ed.). Cengage.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
National Institute of Standards and Technology. (2012). NIST/SEMATECH e-handbook of statistical methods. https://www.itl.nist.gov/div898/handbook/
Welch, B. L. (1947). The generalization of "Student's" problem when several different population variances are involved. Biometrika, 34(1-2), 28-35. https://doi.org/10.1093/biomet/34.1-2.28
Reading the BU 321 Unit 6 instructions
For Unit 6, students compare two groups using a two-sample test, usually of means or proportions. Most versions want the groups summarized side by side, the choice of test justified by what was measured and whether the samples are independent or paired, conditions checked for each group, the test carried out with working shown, and the result interpreted for a business decision. Many rubrics ask for a confidence interval for the difference as well as a p-value, and some ask for an effect size. Be clear about the direction of the difference you report. Include a summary table and cite the textbook and the source of any test method in APA 7.
How the BU 321 Unit 6 example is put together
The sample begins with the area manager's decision about moving a driver. A side-by-side table reports sample size, mean, standard deviation, late orders and mean distance for both stores. The test choice section explains why means are compared rather than proportions and why the samples are independent, and it justifies Welch's version with the unequal spreads. Conditions are checked for each sample. The test section works through the standard error, the Welch statistic and its degrees of freedom, then the p-value and the interval. The final section reads the interval as a decision, reports a small effect size, recommends against moving the driver yet and estimates the sample size needed to narrow the interval.
BU 321 Unit 6 rubric: what full points look like
The rubric for the comparison paper typically weighs the descriptive comparison, the justification of the test, correct execution and interpretation. Descriptive comparison earns full points when both groups are summarized before testing so the reader can see the difference being judged. Justification rewards reasoning about the type of measure and independence, including why an alternative test was rejected. Execution is judged by a correct standard error and degrees of freedom, an accurate p-value and, where the instructions allow, an interval for the difference. Interpretation is weighted heavily and rewards papers that avoid treating a non-significant result as proof of no difference, as the sample does with its interval. Effect size and a next step earn additional credit.
BU 321 Unit 6 help: mistakes that cost points
The most common Unit 6 mistake is concluding that two groups are the same because the test was not significant. Another is using a paired test for independent samples, or the reverse. Students often skip the side-by-side summary and jump to the test, so the reader never sees the size of the difference. Some compare proportions when the counts are too small for the normal approximation. Others report only a p-value without an interval, which hides how uncertain the difference is. Finally, check for obvious explanations, such as distance or shift mix, before blaming a store; the sample confirms the two stores' average distances are nearly identical. Report the direction of the difference in words, Eastgate minus Northside, so a reader cannot misread which store was slower.
Get a BU 321 Unit 6 example written to your instructions
Send the Unit 6 instructions and the rubric from your BU 321 classroom, with the dataset and the two groups the assignment names. We write a custom example that summarizes both groups first, argues the test from the measurement, settles independence and reports the difference with a range. First custom sample free, returned in 24 to 48 hours.
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BU 321 Unit 6 questions, answered
How do I know whether my samples are paired?
Ask whether each observation in one group has a natural partner in the other. The same stores measured before and after a change are paired, while two different sets of stores are not. Where the design is genuinely ambiguous, say which reading you took and why, since the choice changes the procedure and a marker will look for that reasoning.
Should the paper report an effect size?
If the instructions ask for one, report it, and if they do not, an interval for the difference does much of the same work and usually sits inside what the course covers. Either way the point is to say how large the gap is rather than only that it exists, since a significant but tiny difference is an expensive misreading.
Can I compare more than two groups this way?
Not by running the same test repeatedly on every pair, which raises the chance of a false alarm with each comparison. Where three or more groups are involved, follow whatever procedure your reading supplies for that case. If the instructions restrict you to two, choose the pair the business question asks about and say why the others were set aside.
Where can I find a free BU 321 Unit 6 sample paper?
Everything in the BU 321 Unit 6 comparison, from the side-by-side table to the decision, can be read above free. If your groups or measures are different, send the assignment and the comparison you need will come back free, generally inside two days.
Should BU 321 Unit 6 report an effect size?
Many rubrics reward it. The sample reports a standardized difference of about 0.29, a small effect, alongside the p-value and interval. An effect size helps a manager see whether a difference would matter even if it were real.