| Course | GB513 Business Analytics |
|---|---|
| Unit | Unit 5 |
| Paper type | Confidence interval analysis |
| 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 GB513 Unit 5
Sixty-Four Members and a Premium Tier: A Unit 5 Confidence Interval Analysis for a Fitness Club Chain
[Student Name]
Purdue University Global
GB513: Business Analytics
Unit 5 Confidence Interval Analysis
[Instructor Name]
[Date]
The fitness club chain, its survey and every figure are composite and illustrative; the methods cited are real.
The Business Question
Northline Fitness runs five clubs with about 2,400 members each. It is considering a premium tier, $20 a month on top of standard dues, giving access to a recovery room with cold plunge tubs, compression boots and massage chairs. The equipment lease and staffing would cost about $7,200 a month per club. To break even, a club needs 360 premium members, about 15 percent of its membership. The operations director, Lena Ortiz, wants to know whether enough members would sign up and how heavily they use the club now.
The Survey
The chain emailed a short survey to a random sample of members at its largest club, and 64 responded. Members reported their average visits per month over the past three months and answered whether they would pay $20 a month for the premium tier. The sample is small, drawn from one club and limited to members who answered email, so it may overrepresent engaged members.
Interval 1: Average Monthly Visits
The population standard deviation of visits is unknown, so the interval uses the t distribution (Anderson et al., 2020).
Sample mean: 9.4 visits a month. Sample standard deviation: 3.8. Sample size: 64. Critical value: t with 63 degrees of freedom at 95 percent, 1.998. Margin of error: 1.998 times the standard error of 0.475, or 0.95.
The 95 percent confidence interval is 8.45 to 10.35 visits a month.
For the operations director. With 95 percent confidence, the average member at this club comes in between about eight and a half and ten times a month. That is two to three visits a week, frequent enough that a recovery room would be used regularly by the members who buy access.
Interval 2: Share Willing to Pay
Twenty-three of 64 respondents, 35.9 percent, said they would pay $20 a month. Before using the normal approximation, the conditions were checked: 23 yes and 41 no answers, both above 10 (Levine et al., 2021).
Sample proportion: 0.359. Standard error: the square root of 0.359 times 0.641 divided by 64, or 0.0600. Critical value: 1.96, giving a margin of error of 0.118.
The 95 percent confidence interval is 24.1 to 47.7 percent.
For the operations director. With the same confidence, somewhere between about a quarter and nearly half of members would say they would pay for the premium tier. Even the low end of the interval, 24 percent, is well above the 15 percent the club needs to break even.
The lowest plausible share of members willing to pay is still above the break-even share, which is a stronger result than the point estimate alone.
Why Two Intervals
The two intervals answer different parts of the director's question. The proportion interval addresses revenue: will enough members pay to cover the equipment? The visits interval addresses use: will members who pay actually come often enough to value the room, renew and tell others? A tier that sells well but goes unused would lose members after a few months. Together, the intervals suggest the tier would both sell and be used, which is a stronger case than either alone.
Using the Intervals for Planning
The intervals also help with capacity. If 24 to 48 percent of 2,400 members joined, the tier would have about 580 to 1,150 members. At nine to ten visits a month, and assuming premium members use the recovery room on about a third of their visits, the room would see roughly 1,700 to 3,800 sessions a month, or about 60 to 125 a day. Planning for the middle of that range, about 90 sessions a day, would set the number of compression boots and plunge tubs.
A Caution About Stated Intentions
Saying yes on a survey is not the same as paying. James Evans notes that survey responses about future purchases tend to overstate actual behavior (Evans, 2020). If only half of those who said yes actually sign up, the share would fall to about 18 percent, still above break-even but with a thin margin. That argues for a limited launch rather than rolling the tier out at all five clubs at once.
How Many Responses a Firmer Answer Would Need
For an estimate of the paying share that is no more than five points off either way, again at 95 percent confidence, the standard formula, using the current estimate of 0.359 as the planning value, calls for about 354 members. The current interval is wide because 64 is a small sample. A survey of about 354 members across all five clubs would also show whether the largest club is typical.
Recommendation
Northline should launch the premium tier at its largest club for six months, track actual sign-ups against the 360-member break-even and survey about 354 members across all clubs before deciding on the other four.
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.
Evans, J. R. (2020). Business analytics: Methods, models, and decisions (3rd ed.). Pearson.
Levine, D. M., Stephan, D. F., & Szabat, K. A. (2021). Statistics for managers using Microsoft Excel (9th ed.). Pearson.
Reading the GB 513 Unit 5 instructions
In GB513 Unit 5 you build confidence intervals to support a business decision. State the decision and the figure that would make it worthwhile, such as a break-even share. Describe the sample and its limits. For a mean, use t whenever the true standard deviation must be estimated from the sample, and show the sample mean, standard deviation, size, critical value and margin of error. For a proportion, check the conditions for the normal approximation first. After each interval, write a paragraph for the decision maker that compares the interval, especially its lower end, with the threshold. Explain what the intervals mean for planning, note any bias such as stated intentions, and calculate the sample size a narrower interval would need. End on a recommendation; about four pages plus an Excel appendix is usual, citing statistics sources in APA 7.
How this GB513 Unit 5 example is built
The analysis sets Northline Fitness's break-even at 360 premium members per club, about 15 percent of 2,400, against $7,200 a month in equipment and staff. The survey of 64 members at the largest club is described with its limits. The visits interval uses t with 63 degrees of freedom and a 1.998 critical value, citing Anderson and colleagues. The proportion interval checks 23 yes and 41 no answers, citing Levine, Stephan and Szabat, and the highlighted sentence explains why the lower bound carries the decision. Sections explain what each interval contributes and estimate about 60 to 125 recovery room sessions a day. Evans cautions that stated intentions overstate purchases. A sample size of about 354 is calculated, and the recommendation launches at one club for six months.
GB513 Unit 5 rubric: what earns full points
GB513 rubric points for this analysis go to correct intervals and interpretation tied to the decision. Instructors check that the t distribution is used for the mean and that the conditions for the proportion interval are checked. Inputs should be shown so the arithmetic can be followed. The strongest papers compare the interval's ends, especially the lower bound, with the decision threshold rather than reporting the center alone. Explaining what each interval adds, and noting biases such as stated intentions, shows judgment. A sample size calculation for a target margin of error shows planning. A recommendation that reflects the uncertainty earns credit. Citations in APA 7 support the t interval, the proportion conditions and the caution that stated intentions run ahead of purchases.
GB513 Unit 5 help: mistakes that cost points
Many GB513 Unit 5 papers compute intervals correctly and then report only the point estimate in the conclusion. Others use z for a mean with an unknown standard deviation or skip the conditions for a proportion. A frequent gap is the threshold: an interval only supports a decision once it is compared with the figure that matters, such as break-even. Some writers ignore the gap between what people say and what they buy. State the decision and threshold, build each interval with its inputs, compare the ends with the threshold, explain limits and biases, size a better sample and recommend with the uncertainty in view.
Get a GB513 Unit 5 example written to your instructions
Your own survey or sample data, plus the Unit 5 prompt and rubric from GB513, are the inputs. A custom interval analysis built on them arrives in 24 to 48 hours, with every critical value sourced and every interval compared with the threshold your scenario sets. The first request costs nothing. 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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GB513 Unit 5 questions, answered
When should the confidence interval use t instead of z?
For a mean, use t whenever the population standard deviation is unknown, which is nearly always the case with real business data. For a proportion, the normal z value is standard once the success and failure counts are large enough. A finished GB513 example states which applies and why in one sentence, so the choice never looks accidental.
What confidence level should the interval use if the prompt does not say?
Ninety-five percent is the convention and the safest default. Some scenarios justify ninety or ninety-nine, and a strong paper says why: a costly, irreversible decision might call for more confidence and a wider interval. Whatever the level, keep it consistent across both intervals unless the prompt asks you to compare levels directly.
Is it enough to say the interval is between two numbers?
Not in this course. The interval is the evidence; the conclusion is what it means for the decision. The example states the interval, then compares both ends with the break-even figure and says whether the decision holds across the whole range. When one end falls below the threshold, the paper says the data cannot yet support the move.
Where can I find a free GB513 Unit 5 sample paper?
This page carries a full GB513 Unit 5 confidence interval analysis for a fitness club premium tier, with intervals for mean visits and willingness to pay, a required sample size and APA 7 references.
Why does the lower bound of the proportion interval matter most?
The club breaks even at 15 percent of members. Even the lowest plausible share willing to pay, about 24 percent, is above that, which is stronger support for the decision than the point estimate of 36 percent alone.