Petrus's Mobile Car Wash: Testing a Survey Before Spending Savings
Petrus Amukoto plans a mobile car wash in Oshakati. A trailer, water tank, pump and generator will cost NAD 90,000, which is all his savings. To test demand he stood outside a shopping mall on two Saturdays and questioned 40 people. Thirty-one (78%) said they would use a mobile wash, and 24 of those said they would pay NAD 60 for a full wash. He therefore plans to charge NAD 45, expecting 30 cars a day, six days a week, on the strength of the survey. Two fixed car washes in town charge NAD 70 and NAD 90; a filling station offers a free basic wash with a NAD 500 fuel purchase. The mall has parking for 400 cars and attracts mainly weekend shoppers; ten of the 40 people he questioned did not own a car. His cousin, who runs a taxi, says 'everyone in Oshakati wants a clean car'. Petrus wants to order the trailer next week.
1. Assess what the survey evidence can and cannot support. Identify the specific design faults and the quantitative uncertainty.
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What it supports: a general willingness to talk about car washing among Saturday mall shoppers. That is all.
Fault 1 - sample. Forty people at one mall on two weekend days is a convenience sample of shoppers, not of car owners or of people with disposable income for a wash. Ten respondents had no car, so at most 30 answers were even relevant; one enthusiastic non-owner can inflate the 'yes' rate by 3.3 percentage points.
Fault 2 - precision. With n = 40 and 78% saying yes, the 95% margin of error is about ±13 percentage points (1.96 × √(0.78 × 0.22 / 40) ≈ 0.128). The true proportion could be anywhere from 65% to 91%. That band is too wide to build a NAD 90,000 purchase on.
Fault 3 - stated intent is not purchase. Saying 'I would use it' costs nothing. Thirty-one intentions do not equal 31 paying customers, and there is no evidence about frequency - once a month or once a week changes everything.
Fault 4 - the price question is unusable. He asked about NAD 60, got 24 yeses, then set his price at NAD 45 - a 25% discount to his own evidence, for no stated reason. The question was also unpriced against alternatives: respondents were not asked what they currently pay or what they would give up.
Conclusion: the survey cannot support 30 cars a day. It justifies only a cheap, reversible test.
2. Design a research plan that would give Petrus defensible demand estimates before he commits NAD 90,000. Include the numbers you would target and the pricing test.
Read the worked answer
1. Define the customer. Target owners of cars worth washing - minibus taxis, company fleets, salaried commuters. Ignore shoppers without cars.
2. Sample properly. At least 150 completed interviews across four locations: two office parks at 07:30–09:00, one taxi rank, one residential area on a Saturday. Stratify by vehicle type. At n = 150 the margin of error on a 60% estimate falls to about ±8 points.
3. Ask about behaviour, not opinion. 'When did you last wash your car? Where? What did you pay? How long did it take you?' Past behaviour predicts future spending far better than a yes/no intention.
4. Sell before building. The strongest evidence is a prepaid voucher: offer a NAD 60 wash for NAD 40 in advance, redeemable at a fixed site on a fixed weekend. Count vouchers actually sold, not promises. Selling 60 vouchers in four weekends proves willingness to pay; selling 12 does not.
5. Run a price ladder. Test NAD 45, NAD 60 and NAD 75 on separate weekends or sites and record conversion and revenue per hour, not just volume. If NAD 60 converts at 80% of the NAD 45 rate, the higher price wins.
6. Cost the unit economics. Water, soap and fuel per wash plus 25 minutes of an assistant's time at NAD 30 an hour is roughly NAD 24.50. At NAD 45 contribution is NAD 20.50; at NAD 60 it is NAD 35.50. He needs about 122 washes a month to cover NAD 2,500 trailer depreciation alone.
7. Competitive check. Mystery-shop both fixed washes and time the filling-station queue. Their weakness (waiting time) is his selling point.
Decision rule: order the trailer only if voucher sales and the ladder imply at least 100 paid washes a month at NAD 55 or more.