| Course | BU 321 Business Statistics |
|---|---|
| Unit | Unit 4 |
| Paper type | Confidence interval report |
| Length | About 980 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 4
Between 23.6 and 25.7 Minutes: A Confidence Interval Report on a Composite Pizza Chain's Delivery Times and On-Time Rate, Worded for a Manager
Student Name
Business, Herzing University
BU 321: Business Statistics
Instructor Name
March 4, 2026
Between 23.6 and 25.7 Minutes: A Confidence Interval Report on a Composite Pizza Chain's Delivery Times and On-Time Rate, Worded for a Manager
The course's composite pizza business, Brickoven Express, wants to estimate two things about all of its deliveries, not just the 240 orders sampled in October 2025: the average delivery time and the proportion of deliveries that arrive within its 35-minute promise. This report builds a confidence interval for each. It names each quantity as a population value, checks the conditions one at a time against the data, shows every piece of the calculation so a reader can rebuild it, reports each interval with its level and assumptions and then spends the most space on how to say what the intervals mean.
The Quantities Being Estimated
The first quantity is the population mean delivery time, written as the Greek letter mu: the average time from order to doorstep across all Brickoven deliveries during the period the sample represents. The second is the population proportion of deliveries arriving within 35 minutes, written as p. The sample figures, a mean of 24.62 minutes and a proportion of 0.904, are estimates of these values, not the values themselves. Keeping that distinction clear is what separates a correct interval report from one that describes the sample and calls it a conclusion.
Checking the Conditions
For the mean, a t interval requires a random sample, independent observations and a sampling distribution of the mean that is approximately normal (Anderson et al., 2020). The sample was drawn at random from each store's order records, 40 orders per store. Independence is reasonable because 240 orders are a small fraction of the chain's deliveries over two weeks, well under 10 percent. Normality of the sampling distribution is supported by the sample size of 240 and by the data's modest skewness of 0.48; with a sample this large, the central limit theorem makes the t procedure reliable even for moderately skewed data (National Institute of Standards and Technology, 2012).
For the proportion, the interval requires a random sample, independence and enough successes and failures for the normal approximation. The sample contains 217 on-time deliveries and 23 late ones, both above the usual minimum of 10. One qualification applies to both intervals: the sample took 40 orders from each store regardless of store volume, so the intervals describe deliveries with each store weighted equally. If the stores' volumes differ greatly, a chainwide figure would need weighting.
Building the Interval for the Mean
The sample statistics are n = 240, sample mean = 24.62 minutes and sample standard deviation s = 8.25 minutes. The standard error of the mean is s divided by the square root of n: 8.25 divided by 15.49 = 0.533 minutes. For a 95 percent interval with 239 degrees of freedom, the t critical value is 1.970, taken from the t distribution (in Excel, T.INV.2T(0.05, 239)). The margin of error is 1.970 times 0.533 = 1.05 minutes.
At 95 percent confidence, then, mean delivery time is estimated as 24.62 plus or minus 1.05, or from 23.57 to 25.67 minutes. For comparison, a 99 percent interval uses a critical value of 2.597 and runs from 23.23 to 26.00 minutes. The higher level of confidence costs width, as it always does.
Building the Interval for the Proportion
The sample proportion is 217 divided by 240 = 0.904. Taking 0.904 times 0.096, dividing by 240 and taking the square root gives a standard error of 0.0190. For 95 percent confidence the critical value from the standard normal distribution is 1.96, so the margin of error is 1.96 times 0.0190 = 0.037. The 95 percent confidence interval for the on-time proportion is 0.904 plus or minus 0.037, or from 0.867 to 0.941, that is, from 86.7 to 94.1 percent.
| Quantity | Estimate | Standard error | Critical value | 95% interval |
|---|---|---|---|---|
| Mean delivery time (minutes) | 24.62 | 0.533 | t = 1.970 (df 239) | 23.57 to 25.67 |
| On-time proportion | 0.904 | 0.0190 | z = 1.96 | 0.867 to 0.941 |
What the Intervals Mean
The sentence most drafts write is: "The true average delivery time has a 95 percent chance of falling between 23.57 and 25.67 minutes." That sentence is tempting and wrong. After the bounds are computed, the unknown average is simply inside them or outside them; the 95 percent is a property of the procedure, not of this one interval. In a study of researchers and students, Hoekstra et al. (2014) found that most endorsed at least one false statement of this kind, including experienced researchers, which shows how easily the error is made.
The correct sentence is: "We are 95 percent confident that Brickoven's average delivery time is between 23.6 and 25.7 minutes, meaning that intervals built this way would capture the true average in about 95 of every 100 samples." For a manager, the sentence that matters is simpler still: the chain's typical delivery takes about 24 to 26 minutes, and the data do not support a claim that the average is over 26 minutes. That is useful because the chain's franchise agreement, discussed in the next unit, sets a standard of an average below 26 minutes.
For the proportion, the manager's sentence is: between about 87 and 94 percent of Brickoven's deliveries arrive within the 35-minute promise, so roughly one order in eight to one in seventeen runs late. The interval does not say how late, and it does not say which stores or trips account for the late orders; those questions need the analysis in later units.
Does the Report Need a Recommendation?
A confidence interval report estimates; it does not decide. This report therefore makes no operating recommendation, but it points to two decisions the intervals inform. The upper bound of the mean interval, 25.67 minutes at 95 percent confidence, sits below the franchise standard of 26 minutes, which suggests the chain meets it, a question the hypothesis test in Unit 5 addresses formally. The on-time interval, with a lower bound near 87 percent, gives the owners a realistic range to use if they advertise the 35-minute promise. No real restaurant or customer stands behind these figures.
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.
Hoekstra, R., Morey, R. D., Rouder, J. N., & Wagenmakers, E.-J. (2014). Robust misinterpretation of confidence intervals. Psychonomic Bulletin & Review, 21(5), 1157-1164. https://doi.org/10.3758/s13423-013-0572-3
National Institute of Standards and Technology. (2012). NIST/SEMATECH e-handbook of statistical methods. https://www.itl.nist.gov/div898/handbook/
Reading the BU 321 Unit 4 instructions
The Unit 4 report asks you to construct and interpret confidence intervals for business data, usually for a mean and a proportion. Most versions want the parameter identified, conditions checked, the interval calculated with its components shown, and an interpretation written for a nontechnical reader. Many rubrics specify the confidence level or ask you to compare two levels. Instructors pay close attention to wording, since the most common error is describing the interval as a probability statement about the parameter. Some sections ask whether the result supports a decision. Present calculations in a table where possible, with APA 7 citations for the textbook and any other source.
Inside the BU 321 Unit 4 example
The sample first defines the two population quantities and distinguishes them from the sample figures. A conditions section checks randomness, independence, sample size and success counts, and notes a qualification from the equal-per-store design. The mean interval is built step by step with a t critical value of 1.970, and a 99 percent version is added to show the cost of more confidence. The proportion interval follows with its standard error and z value. A summary table holds both. The longest section interprets the intervals, contrasting the tempting sentence with the correct one and ending with manager-ready statements. A short section explains why the report estimates rather than recommends.
BU 321 Unit 4 rubric: what full points look like
The rubric for this unit usually weighs correct identification of the parameter, the condition checks, accuracy of the calculations and quality of interpretation. Parameter points depend on naming a population value rather than restating a sample figure. Condition checks earn full credit when each is tested against the data with a number. Calculations are judged by the correct standard error, critical value and bounds, all shown. Interpretation is often weighted most heavily and rewards wording that attributes the confidence to the method, avoids probability claims about a fixed parameter and translates the result into business terms. The sample's comparison of wrong and right sentences addresses this directly. Tables and APA citations support presentation.
BU 321 Unit 4 help: mistakes that cost points
The most common Unit 4 error is writing that there is a 95 percent probability the true mean lies in the interval. Another is interpreting the interval as the range where 95 percent of individual deliveries fall, which confuses the mean with the data. Students often state that conditions are met without checking them. Some use a z critical value for a mean when the population standard deviation is unknown. Others report bounds without the standard error or critical value, making the result impossible to check. Finally, connect the interval to a decision when the prompt allows; the sample notes that the upper bound sits below a franchise standard, which sets up the next unit.
Get a BU 321 Unit 4 example written to your instructions
Send the Unit 4 instructions and the rubric from your BU 321 classroom, with the dataset or the summary statistics the assignment provides. We write a custom example that checks conditions before building, shows every component, discusses width against its levers and words the interpretation correctly. First custom sample free, back in 24 to 48 hours.
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BU 321 Unit 4 questions, answered
Which critical value should the report use?
That depends on what is known about the population and on the size of the sample, and your reading sets the rule your section grades against. What matters for the report is that the choice gets stated and defended in a line rather than left implied. Where the two candidates would give close bounds, say so and name the one you used.
How should the interval be worded?
Describe the procedure rather than the single range. A wording built around what the method does across repeated samples keeps you inside what the interval supports, while a wording putting a probability on the population value sitting in this range does not. Follow any phrasing your instructions supply, since some sections mark that sentence directly.
Does the report need a recommendation?
Read the prompt, since sections differ. Where one is asked for, keep it downstream of the interpretation and make it sensitive to the whole range rather than to the midpoint. Advice that only works if the true value sits at the center of the interval has ignored the reason for reporting a range at all.
Where can I find a free BU 321 Unit 4 sample paper?
The BU 321 Unit 4 report is published above at no charge, including both intervals and the interpretation section. If you need intervals built from a different dataset, attach it to the prompt and we will build the report on your numbers free, normally within 48 hours.
How should a BU 321 Unit 4 interval be worded?
Attribute the confidence to the method. The sample writes that it is 95 percent confident the average lies in the interval, meaning intervals built this way capture the true value in about 95 of 100 samples. Avoid saying there is a 95 percent probability the true mean is inside.