| Course | GB701 Business Statistics |
|---|---|
| Unit | Unit 5 |
| Paper type | Confidence interval exercise |
| Length | About 850 words, 6 pages double-spaced |
| Format | APA 7 student paper |
| School | Purdue University Global |
| Program | MBA |
| Updated | October 2026 |
Free sample paper for GB701 Unit 5
Two Intervals That Can Be Checked and Two That Cannot: A Unit 5 Confidence Interval Exercise
[Student Name]
Purdue University Global
GB701: Business Statistics
Unit 5 Confidence Interval Exercise
[Instructor Name]
[Date]
The distributor, its accounts and every figure are composite and illustrative; the methods and sources cited are real.
The Sample, Accounted For
The Unit 4 plan drew 234 accounts, 66 special-order and 168 stock-order. Thirteen were excluded because a portal login was shared across several of the customer's branches, making portal use impossible to attribute, and five because their quote histories were incomplete after a system migration. That leaves 216 accounts, six fewer than the 222 the plan's 6 percent allowance would have left, because exclusions ran to 7.7 percent. The shortfall is reported here and its effect on power is revisited in Unit 7.
Interval 1: Mean Quote-to-Order Time
The sample mean is 8.44 days, with a standard deviation of 4.63. The standard error is 4.63 divided by the square root of 216, or 0.315 days. With 215 degrees of freedom, the critical t value is 1.971, so the 95 percent interval runs from 7.82 to 9.06 days.
The full quoting-system extract gives the frame mean as 8.55 days, which falls inside the interval. The interval did what an interval is supposed to do. Because the sample is about 17 percent of the frame, the interval is slightly wider than it needs to be; applying the finite population correction (Lohr, 2019) would narrow it to about 7.88 to 9.00.
Interval 2: Median Quote-to-Order Time
The sample median is 7.50 days. No simple formula gives a reliable standard error for the median of a skewed distribution, so the interval comes from a percentile bootstrap: 5,000 resamples of 216 accounts drawn with replacement from the sample, the median computed for each, and the 2.5th and 97.5th percentiles taken as limits (Efron & Tibshirani, 1993). The interval runs from 6.85 to 7.90 days. The frame median, 7.50, falls inside.
Interval 3: Share of Accounts Using the Portal
Nobody at the distributor knew how many accounts request quotes through the portal, because the portal's logs record logins rather than accounts. Of the 216 coded accounts, 74 used the portal for at least half of their quote requests, a share of 34.3 percent.
The interval uses the Wilson score method. Its limits are 28.2 and 40.8 percent. The more familiar Wald interval, which adds and subtracts 1.96 standard errors from the observed proportion, gives 27.9 to 40.6 percent, nearly the same here. Brown et al. (2001) showed that the Wald interval's actual coverage can fall well below 95 percent even in moderately large samples, especially when the proportion is far from one-half, while the Wilson interval holds its coverage much better. Using Wilson by default avoids having to judge case by case whether Wald is safe.
Interval 4: Share of Accounts with Heavy Revision
The second new quantity is the share of accounts with three or more quotes in the year that went through at least three revision rounds before the customer ordered. Of the 216 accounts, 56 met that definition, 25.9 percent, with a Wilson interval of 20.5 to 32.2 percent.
An interval that captured a known value earns the method some trust when the next interval's target cannot be seen.
How the New Figures Will Be Used
The portal estimate will be reported to the vice president of sales with its interval, not as a single figure. If she plans a campaign to move customers onto the portal, the interval tells her the starting point is somewhere between about 28 and 41 percent of accounts, which is enough to set a target but not to promise one. The revision estimate will feed the regression in Unit 8, where the number of heavily revised quotes enters as a predictor, and its interval reminds the analysis that the variable itself was measured from a sample. Reporting both quantities as intervals from the start also prevents a habit the dashboard encouraged: quoting a single figure as if it were exact.
What the Intervals Say Together
The two checkable intervals both captured their targets, which supports, though it cannot prove, that the sample is representative of the frame. The two new estimates give the sales team figures it never had: about a third of accounts quote through the portal, and about a quarter put quotes through heavy revision. Both figures carry intervals about six to seven points wide on each side, which is precise enough to plan with but not to compare small subgroups.
Limits
The sample is stratified by order type but not by size, so very large accounts may be over- or underrepresented by chance. The portal measure depends on a coding rule, at least half of quote requests, that a different threshold would change. And the intervals describe the sample's frame, active accounts in one twelve-month period, not accounts in other years. If portal use grows, as the sales team hopes, next year's share will differ, and the estimate should be repeated rather than carried forward.
References
Brown, L. D., Cai, T. T., & DasGupta, A. (2001). Interval estimation for a binomial proportion. Statistical Science, 16(2), 101-133. https://doi.org/10.1214/ss/1009213286
Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. Chapman & Hall.
Lohr, S. L. (2019). Sampling: Design and analysis (2nd ed.). CRC Press.
GB701 Unit 5 instructions, in plain terms
The fifth GB701 assignment asks you to estimate quantities from your sample and report how precisely each is known. Account for the sample first: how many were drawn, how many were excluded and why. Compute intervals suited to each quantity: a t interval for a mean, a resampling interval for a median of skewed data and a score interval for a proportion. Show the working for each. Where the true value is known, check whether the interval captured it. Explain any methodological choice a reader might question, such as using Wilson rather than Wald. Say how each estimate will be used and state the limits. About five pages with a results table and one figure, cited in APA 7, is typical.
Inside the GB701 Unit 5 example
The exercise accounts for the sample: 234 drawn, 13 excluded for shared portal logins and 5 for incomplete histories, leaving 216 and a small shortfall against the plan. Interval 1 shows the t calculation and the frame mean inside it, with a finite population note citing Lohr. Interval 2 uses a 5,000-resample percentile bootstrap, citing Efron and Tibshirani. Interval 3 estimates portal use with the Wilson method and compares the Wald interval, citing Brown, Cai and DasGupta. Interval 4 estimates heavy revision, and the highlighted sentence explains how checked intervals earn trust. A section explains how the vice president of sales will use the estimates, and limits close the exercise.
GB701 Unit 5 rubric: what earns full points
Points in the GB701 interval exercise go to choosing the right interval for each quantity. Accounting for the sample, including exclusions and any shortfall, earns credit for transparency. Working shown for each interval demonstrates understanding rather than button-pressing. Using a resampling method for a skewed median and a score method for proportions shows awareness of when standard formulas fail, and justifying those choices carries weight. Checking intervals against known values where possible is unusual and impressive. Explaining how estimates will be used, with uncertainty attached, shows the writer is reporting for a reader. A tidy results table and APA 7 references for the bootstrap and Wilson methods finish the grade.
GB701 Unit 5 help from the desk
Many GB701 interval exercises apply the same t formula to every quantity, including medians and proportions, where it can mislead. Others report intervals without saying how many cases were excluded. A common error is interpreting a 95 percent interval as having a 95 percent chance of containing the true value. Writers often use the Wald interval for proportions without considering its known weaknesses. Few say how the estimates will be used. Account for your sample, match each interval to its quantity, show the working, check against known values if you can, justify unusual choices, describe the use and state the limits. A free custom interval exercise from your own data is available on request.
Get a GB701 Unit 5 example written to your instructions
Upload your data, or the summary statistics your section supplied, with the Unit 5 instructions and rubric. Each interval method gets matched to its quantity and defended, and each result becomes a sentence a manager could act on, in a custom exercise ready in 24-48h. The first sample is free of charge. 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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GB701 Unit 5 questions, answered
Which interval suits a skewed variable?
For the mean, a t interval usually holds up once the sample reaches a few dozen observations, because the sampling distribution of the mean is far less skewed than the data. For the median or a percentile, a bootstrap is the common choice. Whatever is used, a sentence explaining why it fits the variable is what instructors look for first.
How should a 95 percent confidence interval be interpreted?
As the product of a method that, repeated over many samples, captures the true value about 95 percent of the time. Any single computed interval either contains the value or does not. A safe written form says the data are consistent with values between the two limits, which avoids the probability misstatement instructors correct most often.
Is a bootstrap acceptable if the textbook never covers it?
Usually, provided the method is described clearly and cited. State the number of resamples, the type of interval, percentile or bias-corrected, and the software used. Some instructors prefer a formula-based method as the primary result, with the bootstrap as a check, so reading your instructions before choosing is worthwhile.
Where can I find a free GB701 Unit 5 sample paper?
This page includes a full GB701 Unit 5 confidence interval exercise with a t interval and bootstrap interval checked against known values, and Wilson intervals for two newly measured proportions.
Why use the Wilson interval for a proportion?
Its actual coverage stays close to 95 percent across sample sizes and proportions, while the familiar Wald interval can fall well short, especially for proportions far from one-half.