| Course | BU 321 Business Statistics |
|---|---|
| Unit | Unit 5 |
| Paper type | Hypothesis test write-up |
| Length | About 1,010 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 5
Does the Chain Deliver in Under 26 Minutes on Average? A One-Sample Hypothesis Test Write-Up for a Composite Pizza Chain's Franchise Standard
Student Name
Business, Herzing University
BU 321: Business Statistics
Instructor Name
March 18, 2026
Does the Chain Deliver in Under 26 Minutes on Average? A One-Sample Hypothesis Test Write-Up for a Composite Pizza Chain's Franchise Standard
The Business Question
Brickoven Express, the fictional Columbus pizza franchisee studied all term, operates under a franchise agreement with a regional brand. The agreement requires each franchisee to show, at renewal, that its average delivery time is below 26 minutes. The owners want to know whether their October 2025 sample of 240 orders supports that claim for their deliveries as a whole.
The Hypotheses
The claim the owners want to support, that the average is below 26 minutes, becomes the alternative hypothesis, because a hypothesis test can gather evidence for an alternative but can never prove a null. The hypotheses are about the population mean delivery time, mu, not about the sample mean:
Null hypothesis, H0: mu is greater than or equal to 26 minutes.
Alternative hypothesis, Ha: mu is less than 26 minutes.
The two statements are mutually exclusive and together cover every possible value of mu. The test is one-tailed, in the lower direction, because only evidence that the mean is below 26 would support the franchise claim; a mean far above 26 would not help the owners, and a two-tailed test would spread the rejection region across a direction that answers a different question (Anderson et al., 2020).
The Significance Level, Set Before Any Calculation
The significance level is set at 0.05 before the test statistic is computed. The level is the probability of rejecting the null hypothesis when it is actually true, which here means concluding that the chain meets the standard when in fact its average is 26 minutes or more. The franchise agreement names 5 percent as the accepted level, and the owners have no reason to demand stronger evidence, since the consequence of a mistaken claim would be discovered at the next annual review rather than causing lasting harm. Setting the level first prevents the temptation to choose a level after seeing the result.
Checking the Conditions
A one-sample t test requires a random sample, independent observations and an approximately normal sampling distribution of the mean. The sample was randomly drawn from each store's order records. The 240 orders are far fewer than 10 percent of the chain's deliveries in the period, so independence is reasonable. The sample size of 240, together with a modest skewness of 0.48 in delivery times, lets the central limit theorem carry the sample mean's distribution close to a normal shape (National Institute of Standards and Technology, 2012). As noted in Unit 4, the sample gives each store equal weight, which the franchisor accepts because its standard applies to every store.
The Test Statistic and the Decision Rule
The decision rule is stated before the result appears: reject the null hypothesis if the test statistic falls below the critical value of minus 1.651, which is the lower 5 percent point of the t distribution with 239 degrees of freedom (in Excel, T.INV(0.05, 239)), or equivalently if the p-value is below 0.05.
The sample mean is 24.62 minutes, the sample standard deviation is 8.25 minutes and n is 240. The standard error is 8.25 divided by the square root of 240, which is 0.533. The test statistic is t = (24.62 minus 26) divided by 0.533 = minus 2.60. The p-value, the probability of a sample mean this far below 26 if the true mean were exactly 26, is 0.005 (in Excel, T.DIST(minus 2.60, 239, TRUE)).
| Element | Value |
|---|---|
| Hypothesized mean | 26 minutes |
| Sample mean | 24.62 minutes |
| Sample standard deviation | 8.25 minutes |
| Standard error | 0.533 minutes |
| Test statistic | t = minus 2.60, df = 239 |
| Critical value (lower tail, 0.05) | minus 1.651 |
| p-value (one-tailed) | 0.005 |
The Outcome, Reported Twice
In statistical terms: the test statistic of minus 2.60 is below the critical value of minus 1.651, and the p-value of 0.005 is below the significance level of 0.05, so the null hypothesis is rejected. The sample provides statistically significant evidence that the population mean delivery time is less than 26 minutes.
In the language the owners will use at renewal: the October sample gives strong evidence that Brickoven's deliveries average under 26 minutes, meeting the franchise standard. The consistent result from Unit 4, where the 99 percent confidence interval for the mean ran from 23.23 to 26.00 minutes, tells the same story from a different angle: even at a demanding level of confidence, the plausible range for the average barely reaches 26.
Had the p-value landed near 0.05, for example at 0.06, the right report would have been that the sample did not provide sufficient evidence at the chosen level, not that the chain fails the standard. A borderline result calls for more data, such as a second two-week sample, rather than for moving the significance level after the fact. Here the p-value is ten times smaller than the threshold, so the conclusion does not depend on a judgment call about where to draw the line.
Errors, Size and What the Result Does Not Say
Two errors are possible in any test. A Type I error here would be concluding that the chain meets the standard when its true average is 26 minutes or more; choosing 0.05 in advance limits that risk to one chance in twenty. The opposite mistake, a Type II error, would leave compliance unproven even though the chain meets the standard; with this sample size and a true mean near 24.6 minutes, that risk is small.
Statistical significance is not the same as practical importance, a point the American Statistical Association made in its statement on p-values, which warned against treating a p-value below a threshold as proof of a meaningful effect (Wasserstein & Lazar, 2016). The estimated margin below the standard is about 1.4 minutes, which is modest. Expressed as a standardized difference, 1.38 minutes divided by the standard deviation of 8.25 minutes is about 0.17, a small effect. The owners should therefore describe the result as clear evidence of compliance by a small margin, not as proof that deliveries are fast. The test also says nothing about individual stores; a store-by-store look, which Unit 6 begins, could find a store that does not meet the standard on its own. The chain and every figure here are invented for teaching.
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.
National Institute of Standards and Technology. (2012). NIST/SEMATECH e-handbook of statistical methods. https://www.itl.nist.gov/div898/handbook/
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
The Herzing BU 321 Unit 5 instructions
The Unit 5 write-up asks you to test a business claim with a hypothesis test, usually a one-sample test of a mean or proportion. Most versions want the claim restated as null and alternative hypotheses about a population parameter, a significance level chosen in advance, conditions checked, the test statistic and p-value calculated with working shown, a decision and an interpretation in plain language. Many rubrics also ask about Type I and Type II errors and about the difference between statistical and practical significance. State whether the test is one-tailed or two-tailed and why. Gather the key figures in one table and give APA 7 citations for your sources.
How the BU 321 Unit 5 example is put together
The sample opens with the franchise requirement as the business question. The hypotheses place the owners' claim in the alternative and explain why the test is one-tailed. The significance level is justified from the franchise agreement before any number is computed. Conditions are checked against the sample, and the decision rule is written before the result. The calculation section shows the standard error and test statistic and names the Excel functions, and a table collects every element. The outcome appears twice, once statistically and once for the owners, and it is tied to the 99 percent interval from Unit 4. A closing section covers errors, effect size and what the test does not show.
Reading the BU 321 Unit 5 rubric
Herzing's rubric for the hypothesis test commonly scores the hypotheses, the procedure and conditions, the calculation and the interpretation, with discussion of errors often a separate criterion. Hypotheses earn full points when they concern a parameter, are mutually exclusive and place the claim correctly. Procedure points reward a significance level set in advance, checked conditions and a decision rule stated before the result. Calculation is judged by the correct statistic, degrees of freedom and p-value. Interpretation carries heavy weight and requires a plain-language conclusion tied to the business question. Instructors also reward discussion of errors and practical significance, which the sample provides with an effect size and a cited caution.
BU 321 Unit 5 help before you submit
The most frequent Unit 5 error is writing hypotheses about the sample mean instead of the population mean. Another is putting the claim to be supported in the null hypothesis, which makes it impossible to find evidence for it. Students often choose the significance level after seeing the p-value or switch from two-tailed to one-tailed to get a significant result. Some stop at rejecting the null and never translate the decision into what the owners should do. Others describe a significant result as proving the claim or as showing a large effect. Finally, remember that failing to reject the null is not proof that it is true; wording matters in both directions.
Get a BU 321 Unit 5 example written to your instructions
Send the Unit 5 instructions and the rubric from your BU 321 classroom, with the dataset and the claim the assignment sets. We write a custom example that states hypotheses about the population, fixes the level first, shows the working and reports the decision in both languages. First custom sample free, back in 24 to 48 hours.
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BU 321 Unit 5 questions, answered
One tailed or two tailed?
Decide from the claim before you see the data and say why in the write-up. A directional claim in the business question supports a one tailed test, while a question about whether anything has changed supports a two tailed one. Switching after the statistic is computed, because the other choice would cross the threshold, is the move markers watch for.
What if the result is close to the threshold?
Report it as it falls and then say what close means. A result just inside or just outside the criterion is worth a sentence about the sample size, about the effect being small, and about what a repeat study would settle. That paragraph usually earns more than the decision itself, which is one word either way.
Do I need to talk about errors?
Where the instructions ask, name both kinds against this particular claim rather than defining them in the abstract: what it would cost the business to act on a false alarm, and what it would cost to miss a real change. Tying the two costs to the decision at hand is what turns a definition into an application.
Where can I find a free BU 321 Unit 5 sample paper?
The finished BU 321 Unit 5 test write-up, with its decision rule, table and plain-language outcome, is available above for free. For a test of your own claim or dataset, describe the claim in your request and a free worked test on it will follow, commonly within two days.
One tailed or two tailed in BU 321 Unit 5?
Let the business question decide. The sample uses a one-tailed test because only evidence that the mean is below 26 minutes supports the franchise claim. If either direction would change the decision, use a two-tailed test, and choose before looking at the data.