MT355 Unit 9 Survey Data Analysis Exercise Example

Every Percentage Carries Its Margin: An MT355 Unit 9 Data Analysis Exercise on Adult Swim Lesson Demand

[Student Name]

Purdue University Global

MT355: Marketing Research and Analytics

Unit 9 Data Analysis Exercise

[Instructor Name]

[Date]

The swim school, responses and figures are composite; the statistical methods and sources cited are real.

Response and Eligibility

Responses came from 731 of 2,940 households, a response rate of 24.9 percent, close to the 24 percent assumed in Unit 7. Of the 731 respondents, 163 could not swim one length, 22.3 percent, close to the 22.5 percent from the soft launch. Every comparison below uses those 163 people, so margins are wide and differences must be large to be trusted. Each comparison answers one of the sub-questions from Unit 2.

Table One: Price

Sub-question two asks how price moves interest.

Each eligible respondent saw one price, assigned at random. The share answering likely or very likely, the top two boxes, was 43.6 percent at $148 (24 of 55, margin about 13.1 points), 33.3 percent at $168 (18 of 54, margin about 12.6 points) and 18.5 percent at $188 (10 of 54, margin about 10.4 points).

A chi-square test of likelihood by price gives 7.99 with two degrees of freedom, p of about 0.018. Were price irrelevant, a spread like this one between the three groups would be very unusual. Because prices were randomly assigned, the differences can be attributed to price rather than to differences between the groups.

The largest drop is between $168 and $188.

Table Two: Pool

Sub-question, implied by the decision: does demand differ between pools?

Near North, 37.1 percent of eligible respondents chose the top two boxes (36 of 97, margin about 9.6 points). Near Riverside, 24.2 percent did (16 of 66, margin about 10.3 points). The chi-square for pool is 3.00 on a single degree of freedom, giving a p value near 0.084. The difference is suggestive but would not meet a conventional 0.05 threshold. North appears stronger, but the data do not rule out chance.

Table Three: Evenings

Sub-question: which evenings would most adults attend?

Tuesday was chosen by 57.7 percent of eligible respondents (94 of 163), Thursday by 50.9 percent (83), Wednesday by 41.1 percent (67) and Monday by 30.7 percent (50). Nineteen respondents, 11.7 percent, chose none of these. Respondents could choose more than one evening.

Table Four: Panel

The opt-in panel recruited 250 eligible adults across 14 ZIP codes. Of these, 38.0 percent chose the top two boxes at the price they saw. Baker et al. (2013) caution that a margin of error assumes random selection, so no margin is reported. The panel figure is broadly similar to the list figure and suggests that interest is not confined to families already connected to the school.

Projection Panel

Stated likelihood overstates actual enrollment. Morwitz et al. (2007) found that the link between purchase intentions and actual purchases varies widely, and is often weak for new products and services. The projection therefore applies a conversion assumption: 27 percent of top-two-box respondents enroll, a figure in the range commonly used for new services and tested in the sensitivity runs below.

Near North, the list holds 1,710 households. At the observed eligibility rate of 22.3 percent, that is about 381 eligible adults. At North's top-two-box rate of 37.1 percent and a 27 percent conversion, projected enrollment is about 38, against a bar of 16.

Near Riverside, 1,230 households give about 274 eligible adults. At 24.2 percent and 27 percent conversion, projected enrollment is about 18, just above the bar.

North clears the bar more than twice over; Riverside clears it by two people, which is a different decision.

What the Barrier Item Shows

Among the 163 eligible respondents, the most common barriers chosen were fear of water, 49 percent; time, 44 percent; embarrassment, 38 percent; and cost, 27 percent. Respondents could choose several. The share choosing embarrassment supports the interview finding about the viewing window, though the survey cannot say how many would be reassured by covering it. Cost ranked fourth, consistent with the price result: price matters at the margin, especially above $168, but it is not the main reason adults have not learned.

Who Responded

Respondents who screened in were more often women, 61 percent, and more often aged 35 to 49, 47 percent, than the list overall. The plan in Unit 7 chose not to weight, so these differences are reported rather than corrected, and the owner should read the results as describing mostly parents in their thirties and forties.

Sensitivity

At a conversion of 15 percent, North projects about 21 and Riverside about 10. At 35 percent, North projects about 49 and Riverside about 23. North stays above the bar under every assumption tested; Riverside falls below it at low conversion. The projection also counts only households on the school's list, so it likely understates demand, since the panel suggests interest exists beyond the list.

Reading the Results Carefully

Malhotra (2019) warns against treating statistical significance as practical importance. The price effect is both significant and practically large. The pool difference is not significant at 0.05, but the projection, which combines the pool difference with list size, gives the owner a practical reason to treat the two pools differently.

References

Baker, R., Brick, J. M., Bates, N. A., Battaglia, M., Couper, M. P., Dever, J. A., Gile, K. J., & Tourangeau, R. (2013). Summary report of the AAPOR task force on non-probability sampling. Journal of Survey Statistics and Methodology, 1(2), 90-143. https://doi.org/10.1093/jssam/smt008

Malhotra, N. K. (2019). Marketing research: An applied orientation (7th ed.). Pearson.

Morwitz, V. G., Steckel, J. H., & Gupta, A. (2007). When do purchase intentions predict sales? International Journal of Forecasting, 23(3), 347-364. https://doi.org/10.1016/j.ijforecast.2007.05.015