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.

5.) Which of the following is the correct statement for the claim?

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

Ho: At least one of the percentages is different

H1: At least one of the percentages is different.

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

6.) The test statistic is:

33.942

31.938

26.963

17.455

7.) The p-value is:

.000000238

.000000539

.000000989

.263122245

8.) The conclusion for this test is:

Fail to 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 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

Answer 1

5.) Which of the following is the correct statement for the claim?

H1: At least one of the percentages is different.

6.) The test statistic is: 31.938

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

State	%	O	E	(O - E)^2/E
Washington	0.51	450	510	7.059
Oregon	0.3	340	300	5.333
Idaho	0.11	150	110	14.545
Montana	0.08	60	80	5.000
Total	1	1000	1000	31.938

Chi square = ∑[(O – E)^2/E]

Chi square = 31.938

7.) The p-value is: 0.000000539

We have n=4, df = n – 1 = 4 – 1 = 3

P-value = 0.000000539

(by using Chi-square table or excel)

8.) The conclusion for this test is:

Here, we get

P-value = 0.000000539 < α = 0.05

So, we reject the null hypothesis H₀

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