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. Suppose that we want to test the claim that the sample of 1000 subjects has a distribution that agrees with the distribution of state populations. Use a significance level of 0.05.

What is the expected value for each state?

Answer 1

Among the four northwestern states,

Expected Population of Washington = 1000*(51/100) = 510

Expected Population of Oregon = 1000*(30/100) = 300

Expected Population of Idaho = 1000*(11/100) = 110

Expected Population of Montana = 1000*(8/100) = 80

	Washington	Oregon	Idaho	Montana
Observed Population	450	340	150	60
Expected Population	510	300	110	80

We perform the chi square goodness of fit test in order to see if the sample of 1000 subjects has a distribution that agrees with the distribution of state populations

H₀: The sample has a distribution same as that of the population

H₁ : The sample and population have different distributions.

The chi square test statistic is given by,

Where is the observed value

and, is the expected value

The critical value is given by,

Here, since

We reject the null hypothesis at level of significance.

Hence, We can conclude at level of significance that the sample of 1000 subjects has a distribution that donot agree with the distribution of state population.