Question

Among the four northwestern states, Washington has 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8%. A market researcher selects a sample of 1000 subjects, with 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana. At the .05 significance level, test the claim that the sample of 1000 subjects has distribution that agrees with the distribution of state populations.

1. Which of the following is the correct statement for the claim?

H1: At least one of the percentages is different.

Ho: At least one of the percentages is different

H1: Wa = .51, Or = .3, Id = .11, Mn= .08

Ho: Wa = .51, Or = .3, Id = .11, Mn= .08

2. The p-value is:

a.000000539

b.000000989

c.263122245

d.000000238

3.

The conclusion for this test is:

a. Fail to reject Ho which says that there is sufficient evidence to support the claim of the same distribution

b.Reject Ho which says there is sufficient evidence to support the claim of the same distribution

c.Fail to reject Ho which says there is sufficient evidence to warrant rejection of the claim of the same distribution

d.Reject Ho which says there is sufficient evidence to warrant rejection of the claim of the same distribution

Answer 1

1) Null and Alternative Hypotheses:

H0 ​: p1​=0.51, p2​=0.30, p3​=0.11, p4​=0.08

H1: At least one of the percentages is different.

2) The following table is obtained:

Categories	Observed	Expected	(fo-fe)2/fe
Washington	450	1000*0.51=510	(450-510)2/510 = 7.059
Oregon	340	1000*0.30=300	(340-300)2/300 = 5.333
Idaho	150	1000*0.11=110	(150-110)2/110 = 14.545
Montana	60	1000*0.08=80	(60-80)2/80 = 5
Sum =	1000	1000	31.938

Test statistic:

df = 4-1 =3

p-value = CHISQ.DIST.RT(31.938, 3) =  0.000000539

3) Conclusion: As p-value < 0.05

d.Reject Ho which says there is sufficient evidence to warrant rejection of the claim of the same distribution