Day

Male

Female

Total

Day 1

760 / 900 = 84.4%

40 / 100 = 40%

1000

Day 2

600 / 700 = 85.7%

150/300 = 50%

1000

On day 1, 1000 people were asked 'Do you like Coke more than Pepsi?'

On day 2 another 1000 people were asked the same question.

The number of people who said yes is recorded in the above table. (E.g. 760 out of 900 males answered 'yes' on day 1.)

Did more people like Coke on day 2 compared to day 1?

[Note: the question is different to the exercise in class, so think carefully.]

Question

Day

Male

Female

Total

Day 1

760 / 900 = 84.4%

40 / 100 = 40%

1000

Day 2

600 / 700 = 85.7%

150/300 = 50%

1000

On day 1, 1000 people were asked 'Do you like Coke more than Pepsi?'

On day 2 another 1000 people were asked the same question.

The number of people who said yes is recorded in the above table. (E.g. 760 out of 900 males answered 'yes' on day 1.)

Did more people like Coke on day 2 compared to day 1?

[Note: the question is different to the exercise in class, so think carefully.]

BlackTom AI · Accepted Answer

Compute the overall proportions directly. Day 1: total "yes" = 760 (males) + 40 (females) = 800 out of 1000 → 800/1000 = 0.80 = 80%. Day 2: total "yes" = 600 + 150 = 750 out of 1000 → 750/1000 = 0.75 = 75%. So fewer people said yes on day 2 (75%) than on day 1 (80%).

Relevant concepts: subgroup proportions, weighted averages, and Simpson’s paradox. Even if each subgroup’s within-group percent can increase, the overall percent can fall if the sample composition (weights) changes.

Step-by-step calculations and intermediate steps:
- Day 1 male rate = 760/900 = 0.844444... = 84.44%
- Day 1 female rate = 40/100 = 0.40 = 40%
- Day 1 overall = (760 + 40) / 1000 = 800/1000 = 0.80 = 80%

- Day 2 male rate = 600/700 = 0.857142... = 85.71%
- Day 2 female rate = 150/300 = 0.50 = 50%
- Day 2 overall = (600 + 150) / 1000 = 750/1000 = 0.75 = 75%

Why the apparently paradoxical situation occurs: both subgroup rates increased from day 1 to day 2 (males 84.44% → 85.71%, females 40% → 50%). However, the proportion of males in the sample fell from 900/1000 = 90% on day 1 to 700/1000 = 70% on day 2, while the female share rose from 10% to 30%. Because males had the higher "yes" rate, shrinking the high-rate group and enlarging the lower-rate group can lower the overall weighted average despite increases within both groups. This is an instance of Simpson's paradox (a change in group sizes reverses the overall trend).

Why "Yes" would be incorrect: the raw totals show 800 yes on day 1 vs 750 yes on day 2; therefore the overall proportion decreased.

Conclusion: No — the number (and proportion) of people who liked Coke was lower on day 2 (75%) than on day 1 (80%), confirming the provided answer "No."

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