Question

According to the Census bureau the distribution by ethnic background of the NYC population in a recent year was

Hispanic 28%

Black 24%

White 35%

Asian 12%

Others 1%

The manager of a large complex in the city wonders whether the distribution by race of the complex's resident is consistent with the population distribution. To find out, she records data from random sample of 800 residents. Table below displays sample data. α=0.05

Race	hispanic	black	white	asian	others
count	212	202	270	94	22

a) state null and alternative hypotheses (write mathematically) and write claim

b) find standardized test statistic

c) Identify the rejection region (critical region) and fail to reject region

d) decide whether to reject or fail to reject the null

e) make an interpretation of your decision in the context

Answer 1

Here the manager want "whether the distribution by race of the complex's resident is consistent with the population distribution".

For this we need to use goodness of fit test.

a) H₀ :  p₁ = 0.28, p₂ = 0.24, p₃ = 0.35, p₄ = 0.12 , p₅ = 0.01

H₁ : At least one group have difference proportion.

b)

Let's do calculation in excel:

e) At 5% level of significance there are sufficient evidence to conclude that the distribution by race of the complex's resident is different than the population distribution