| Course | MST-7000 Managerial Statistics |
|---|---|
| Module | Module 4 |
| Paper type | Module 4 written assignment: confidence intervals, hypothesis testing and sample size |
| Length | About 558 words, 5 pages |
| Format | APA 7 student paper |
| School | Thomas Edison State University |
| Program | MBA in Data Analytics |
| Updated | October 2026 |
Free sample paper for MST 7000 Module 4
How Sure Can We Be? Intervals, a Borderline Test and the Sample Size for a Retailer's Decisions
Student Name
MBA in Data Analytics, Thomas Edison State University
MST-7000: Managerial Statistics
Mentor Name
Month Day, Year
How Sure Can We Be? Intervals, a Borderline Test and the Sample Size for a Retailer's Decisions
Estimating the Mean Order Value
A new sample of 64 orders from this quarter had a mean of $812 and a standard deviation of $340. Because the population standard deviation is unknown, Anderson et al. (2011) recommend the t distribution, with n minus 1 degrees of freedom.
We can be 95 percent confident that the mean order value this quarter lies between about $727 and $897. The interval is wide because order values vary greatly; it does show that the mean has risen above last quarter's sample mean of $686, which falls below the interval. Excel's CONFIDENCE.T(0.05,340,64) returns the same margin of error, which I used to check the hand calculation.
| Step | Value |
|---|---|
| Standard error, 340 / square root of 64 | $42.50 |
| t value for 95 percent, 63 df, T.INV.2T(0.05,63) | 1.998 |
| Margin of error, 1.998 x 42.50 | $84.93 |
| 95 percent confidence interval | $727.07 to $896.93 |
Testing the Return Rate
The company's standard is a return rate of 8 percent or less. This quarter, 41 of 400 sampled orders were returned, a rate of 10.25 percent. The question is whether this is evidence that the true rate now exceeds 8 percent.
The p-value of 0.049 is just below 0.05, so the test rejects the null hypothesis: there is evidence at the 5 percent level that the return rate exceeds 8 percent. The sample size condition is met, since np and n(1 minus p) both exceed 5. A two-tailed test would not have rejected, since its p-value would be 0.097; the one-tailed form fits because only a rise above the standard calls for action.
| Element | Value |
|---|---|
| Null hypothesis | p is at most 0.08 |
| Alternative hypothesis | p is greater than 0.08 |
| Significance level | 0.05 |
| Standard error, square root of 0.08 x 0.92 / 400 | 0.01356 |
| Test statistic z = (0.1025 minus 0.08) / 0.01356 | 1.66 |
| p-value, 1 minus NORM.S.DIST(1.66,TRUE) | 0.049 |
Reading a Borderline Result
A p-value of 0.049 is not strong evidence. Wasserstein and Lazar (2016), writing for the American Statistical Association, caution that p-values do not measure an effect's size or practical weight, and that decisions should not turn on crossing 0.05. Had a single fewer order been returned, the p-value would have been 0.070 and the test would not have rejected. I therefore recommended reviewing returns by product category, which would be useful whatever the test showed, rather than announcing a crisis.
How Large a Sample?
Anderson et al. note that sample size calculations should be rounded up and use a planning value from earlier data. Cohen (1992) adds that studies too small to detect an effect of practical size waste effort; a sample of 865 would estimate the return rate within two percentage points, while the 400-order sample's margin of error is about three.
| Goal | Formula | Sample needed |
|---|---|---|
| Estimate the return rate within 2 points at 95 percent, planning value 0.10 | 1.96 squared x 0.10 x 0.90 / 0.02 squared | 865 orders |
| Estimate mean order value within $50 at 95 percent, s = $340 | (1.96 x 340 / 50) squared | 178 orders |
Recommendations
Report the mean order value as an interval, not a single figure. Treat the return-rate result as a signal to investigate, and draw a sample of 865 orders next quarter to estimate the rate within two percentage points.
References
Anderson, D. R., Sweeney, D. J., & Williams, T. A. (2011). Essentials of modern business statistics with Microsoft Excel (5th ed.). South-Western Cengage Learning.
Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155-159. https://doi.org/10.1037/0033-2909.112.1.155
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
What the MST 7000 Module 4 instructions ask for
The fourth written assignment covers confidence intervals, hypothesis testing and sample size, which also feature in the midterm assignment due by week 5. Expect problems that ask you to build intervals for means and proportions, state hypotheses, compute test statistics and p-values, reach conclusions and calculate sample sizes. Use Excel functions such as T.INV.2T, NORM.S.DIST and CONFIDENCE.T, and show each step. Interpret every interval and every test in plain words, and state what the result means for the decision, not only whether the null hypothesis was rejected. For every test, say which tail or tails it uses and what in the business question calls for that. Keep each calculation in its own labeled cell.
How this MST 7000 Module 4 example is built
The memo builds a t interval for the mean order value in a step table and interprets it against last quarter's figure. A second table sets out a one-tailed test of the return rate with hypotheses, standard error, test statistic and p-value. A section explains why a borderline p-value calls for caution, drawing on the American Statistical Association's statement. A table computes two sample sizes, and research on power explains why the larger sample matters. Recommendations close the memo. The memo also checks the hand-computed margin of error with Excel's CONFIDENCE.T and shows that a two-tailed test would not have rejected, which explains the choice of a one-tailed test.
Where the marks sit in the MST 7000 Module 4 rubric
Mentors grade this assignment on correct intervals, tests and sample sizes, clear statement of hypotheses, appropriate use of t or z and accurate interpretation. Papers that interpret a p-value with care, rather than treating 0.05 as a bright line, show statistical maturity. Checking conditions, such as np greater than 5, demonstrates thoroughness. Connecting each result to a business action, and explaining the interval in words, makes the analysis useful to managers. Justifying a one-tailed or two-tailed test from the business question, and checking calculations with a second Excel function, shows care. Clear step tables let a mentor find any error quickly. Stating conclusions in plain words, alongside the formal decision, completes the analysis.
Common MST 7000 Module 4 mistakes, and how to avoid them
Students lose points by using z when the population standard deviation is unknown, by stating hypotheses about the sample rather than the population, by writing that the null hypothesis is proved or by rounding sample sizes down. Others interpret a 95 percent interval as containing 95 percent of the data. State hypotheses about population parameters. Use t for means with unknown sigma. Say "reject" or "fail to reject." Round sample sizes up. Name the tails your test uses and give the reason. Interpret the interval in words, as a range for the population mean, not for individual orders, and say what it means for planning. A free first sample on your own MST-7000 Module 4 assignment is available on request.
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MST 7000 Module 4 questions, answered
Where can I find a free MST 7000 Module 4 sample paper?
A t interval for order value, a test of a return rate and sample size calculations are worked in the assignment above.
When should a t interval be used instead of z?
When estimating a mean and the population standard deviation is unknown.
What does a p-value measure?
How likely a result this extreme, or more so, would be if the null hypothesis held.
Why is a p-value of 0.049 weak evidence?
It barely crosses the conventional line, and small changes in the data could reverse the conclusion.
How is sample size for a proportion calculated?
Multiply z squared by p and by one minus p, then divide by the margin of error squared, rounding the result up.