A tech company is researching how initial price information affects people’s perception of smartphone value. They show 200 middle school students a new smartphone and split them into two groups:
Group A (100 students): Told the phone normally costs $600, but is on sale.
Group B (100 students): Told the phone normally costs $200, but prices might increase.
Both groups are then asked two questions:
1. What do you think is a fair price for this phone?
2. What’s the maximum you’d be willing to pay for this phone?
Results:
Group A:
– Average fair price: $450
– Average maximum price: $525
– Standard deviation of maximum price: $75
Group B:
– Average fair price: $230
– Average maximum price: $275
– Standard deviation of maximum price: $50
1. Difference in average fair price:
Group A – Group B = $450 – $230 = $220
2. Percentage difference in average maximum price:
Percentage = (Group A – Group B) / Group B × 100
= ($525 – $275) / $275 × 100
= 250 / 275 × 100 ≈ 90.91%
Group A’s average maximum price is approximately 90.91% higher than Group B’s.
3. Range for 95% of Group A’s maximum prices (using empirical rule):
Mean ± 2 standard deviations
$525 ± (2 × $75)
Range: $375 to $675
4. Alignment with empirical rule:
The empirical rule suggests that approximately 95% of data falls within 2 standard deviations of the mean, leaving about 5% outside this range.
Half of this 5% (2.5%) would be above the upper bound.
20% of students paying more than $575 is much higher than the expected 2.5%.
This does not align with what we’d expect based on the empirical rule, suggesting the distribution might be skewed or not follow a normal distribution.
5. Anchoring bias explanation:
The initial price information ($600 for Group A, $200 for Group B) served as an anchor for each group’s perception of the phone’s value. Group A, anchored to a higher price, consistently valued the phone higher than Group B, even though both groups saw the same product. This demonstrates how the first piece of price information significantly influenced students’ judgments about fair and maximum prices, despite having no actual information about the phone’s features or market value.
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