Question

Use the following to answer 5 - 8.

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.

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

Group of answer choices

H1: At least one of the percentages is different.

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

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

Ho: At least one of the percentages is different

Question 6

The test statistic is:

Group of answer choices

17.455

26.963

33.942

31.938

Question 7

The p-value is:

Group of answer choices

.000000238

.000000539

.263122245

.000000989

Question 8

The conclusion for this test is:

Group of answer choices

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

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

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

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

Answer 1

Solution:

Given: Among the four northwestern states,

Washington has 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8%.

Claim: the sample of 1000 subjects has distribution that agrees with the distribution of state populations.

Level of significance = 0.05

Question 5

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

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

Question 6

The test statistic is:

Chi square test statistic for goodness of fit

Where

O_i = Observed Counts

E_i =Expected Counts = N * % = 1000 * % values

Thus we need to make following table

states	Expected %	Oi: Expected Counts	Ei: Expected Counts	Oi^2/Ei
Washington	51%	450	510	397.059
Oregon	30%	340	300	385.333
Idaho	11%	150	110	204.545
Idaho	8%	60	80	45.000
	100%	N = 1000

Thus

Question 7

The p-value is:

Use following Excel command:

=CHISQ.DIST.RT(x, df)

where

x = and df = k - 1= 4 - 1 = 3

thus

=CHISQ.DIST.RT(31.938,3)

= 0.000000539

thus p-value is: 0.000000539

Question 8

The conclusion for this test is:

Since p-value = 0.000000539 < 0.05 level of significance, we reject null hypothesis.

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