Hypothesis and Test Statistic! 11. Among the four northwestern states, Washingto

Question

Hypothesis and Test Statistic!

11. 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 0.05 significance level, test the claim that the sample of 1000 subjects has a distribution that agrees with the distribution of state populations. a. What are the appropriate hypotheses? b. What is the test statistic? (Keep two decimal places) c. What conclusion can be drawn from this test? Make sure to interpret the result in context. (State if the null hypothesis is rejected or not rejected)

Explanation / Answer

a)

Nullhypothesis:

H0 : The distribution of the sample agrees with the population distribution.

Alternative hypothesis:
H1 : It does not agree.

b)significance level =0.05

total sample subjects =1000

test statistic is Xc2 = (Oi – Ei)2 / Ei

state

Population

Oi

Population

Ei

Oi-Ei

(Oi-Ei)2

(Oi-Ei)2 / Ei

Washington

450

0.51*1000 =510

-60

3600

7.058824

Oregon

340

0.30*1000

=300

40

1600

5.33333

Idaho

150

0.11*1000

=110

40

1600

14.54545

Montana

60

0.08*1000

=80

-20

400

5

Total

1000

1000

0

7200

31.93761

the value of the teststatistic is 31.93761 ~ 31.938

state

Population

Oi

Population

Ei

Oi-Ei

(Oi-Ei)2

(Oi-Ei)2 / Ei

Washington

450

0.51*1000 =510

-60

3600

7.058824

Oregon

340

0.30*1000

=300

40

1600

5.33333

Idaho

150

0.11*1000

=110

40

1600

14.54545

Montana

60

0.08*1000

=80

-20

400

5

Total

1000

1000

0

7200

31.93761

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