Question

Researcher A claims to have quantified the drink consumption habits of Coffee Grounds' customers. He claims that the choice of each customer is a random sample from a distribution over five outcomes: Smoothie, Coffee, Milk Tea, Classic Tea, and Sparkling Juice, with probability of 0.2, 0.15, 0.2, 0.4, and 0.05, respectively.

1. Another researcher B rejects one part of the A's claim: he can’t believe customers choose Classic Tea with a 40% probability (he doesn’t care at all about the probabilities of the other choices). State null and alternative hypotheses that he should use to investigate this issue.

Answer 1

Aim: To specify the null and the alternative hypothesis.

Given: The research A claims that 40 % of the population choose classic tea.

Parameter: Let P be the population proportion, so P is the proportion of the people who choose the classic tea. Let P0 be some pre specified value of P , so P0 is 0.4.

Hypothesis:

H0: The proportion of the people who choose classic tea is equal or do not differ significantly from the pre specified value.

v/s

H1:The proportion of the people who choose classic tea is not equal or differs significantly from the pre specified value.

Mathematically,

H0: P = 0.4 v/s H1: P 0.4