Question

The Census Bureau claims that the expected frequency distribution of ethnic background of the New York city population is 42% of Hispanic, 38% of White and 20% of Others. The manager of a large housing complext in the city took a sample from his complex and found that there are 200 Hispanics, 350 Whites and 100 Others. He wanted to test the claim that the actual ethnic backgound distribution from his housing complex agrees with the Census Bureau's claimed distribution using a significance level of 0.05. Answer questions 1-4.

4. State the null and alternative hypotheses.

Question 1 options:

a)	H0: The frequencies of ethnic background of the people in the complex are 42% of Hispanic, 38% of White and 20% of Others. Ha: At least one of the ethnic frequencies is different from the Census Bureau's distribution.

b)	H0: The frequencies of ethnic background of people in the complex are all equal. Ha: At least one of the ethic frequency is different from the others in the complex.

c)	H0: The frequencies of ethnic background of people in the complex are all equal. Ha: The frequencies of ethnic background of people in the complex are all different.

d)

H0: The housing complex is independent of the Census Bureau.

Ha: The housing complex is not independent of the Census Bureau.

5. What is the test statistic? (Choose the closest answer)

Question 2 options:

a)

-0.13

b)

66

c)

69.4

d)

8.97

What is the P-value? (choose the closest one)

Question 3 options:

a)

0.086

b)

0.01

c)

0

d)

0.0306

. State the conclusion.

Question 4 options:

a)	Fail to reject H0: There is insufficient evidence to support the claim that the actual ethnic background distribution from his housing complex agrees with the Census Bureau's claimed distribution.

b)	Reject H0. There is sufficient evidence to support the claim that the actual ethnic background distribution from his housing complex agrees with the Census Bureau's claimed distribution

c)	Reject H0: There is sufficient evidence to warrant the rejection of the claim that the actual ethnic background distribution from his housing complex agrees with the Census Bureau's claimed distribution.

d)	Fail to reject H0: There is insufficient evidence to warrant the rejection of the claim that the actual ethnic background distribution from his housing complex agrees with the Census Bureau's claimed distribution.

Answer 1

1) option A is correct

5)applying chi square goodness of fit test:

		observed	Expected		Chi square
category	Probability(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
Hispanic	0.420	200.000	273.000		19.520
White	0.380	350.000	247.000		42.951
other	0.200	100.000	130.000		6.923
total	1.000	650	650		69.395

test statitic =69.4 ; option C is correct

3)

p value =0.0000

option Cis correct

4)

Reject H0: There is sufficient evidence to warrant the rejection of the claim that the actual ethnic background distribution from his housing complex agrees with the Census Bureau's claimed distribution.