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Do 400 of 1000 sales signal a favourite plan

Question

A streaming service sells three subscription plans AA, BB and CC. Among its first 10001000 sales, 400400 were plan AA. Does this show customers prefer plan AA (i.e. its share exceeds one third)? Reply 11 for yes, 00 for no.

Short answer

11 (yes). Under equal preference p=13p=\tfrac13, the standard error of p^\hat p is 2/91000≈0.0149\sqrt{\tfrac{2/9}{1000}}\approx0.0149, so z=0.4−1/30.0149≈4.47z=\tfrac{0.4-1/3}{0.0149}\approx4.47. The one-sided p-value is a few in a million, so equal preference is rejected.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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