Question

# Use the following to answer 5 - 8. Among the four northwestern states, Washington has 51%...

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?

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:

17.455

26.963

33.942

31.938

Question 7

The p-value is:

.000000238

.000000539

.263122245

.000000989

Question 8

The conclusion for this test is:

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

Solution :

Question 5 :

Null Hypothesis :

H0: Wa = .51, Or = .3, Id = .11, Mn= .08

Alternative Hypothesis :

H1: At least one of the percentages is different.

Question 6

test statistic:

 States percentage Observed Expected (Observed - Expected) ((Observed - Expected)^2) / (Expected) Washington 51% = 0.51 450 0.51 * 1000 = 510 -60 7.058824 Oregon 30% = 0.30 340 0.30 * 1000 = 300 40 5.333333 Idaho 11% = 0.11 150 0.11 * 1000 = 110 40 14.54545 Montana 8%= 0.08 60 0.08 * 1000 = 80 -20 5 Sum = 31.93761

Test Statistic = 31.938 (Option D)

Question 7:

=CHIDIST(31.938,3)

P value : 0.000000539

Option B

Question 8 :

P-value < alpha

So, reject H0 (Null Hypothesis)

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

Option B

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