Answer to Question #221259 in Statistics and Probability for Bali

Question

Suppose that a random
sample of 1,000 people was asked which option they support and their political affiliations. The possible
responses to the question about political affiliation were Democrat, Republican, and Independent (which
included a variety of political persuasions). The responses are summarized in the accompanying table. Do these
results allow us to conclude at the 1% significance level that political affiliation affects support for the economic
options? [10]
Economic
Options
Political Affiliation
Democrat Republican Independent
Cut Spending 102 282 61
Raise Taxes 38 67 25
Inflate the
Economy
131 88 31
Let Deficit
Increase
61 90 25

Answer 1

The claim is that whether the political affiliation affects support for the economic options.

From this information, the null and alternative hypotheses are given by

H₀: The political affiliation affects does not support for the economic options.

H₁: The political affiliation affects support for the economic options.

The level of significance α=0.01

The test-statistic:

$χ^2 = \sum^k_{i=1} \frac{(f_i -e_i)^2}{e_i}$

Where k is the number of cells in the cross-classification table

e_i is the expected frequencies, f_i is observed frequencies.

Using MINITAB, we conduct the above test of the null hypothesis against the alternative hypothesis in the following steps.

1) Type the observed frequencies into adjacent columns.

2) Click Stat, Tables, and Chi-Square (Table in Worksheet)…

3) Select or type the names of the variables representing the columns.

We get the following output:

From the above results we get,

The test statistic

$χ^2 = 70.675$

The P-value is 0.000

Here we observe that, the P-value is less than the level of the significance 0.01, so we have to reject the null hypothesis. Therefore, we conclude that there is sufficient evidence to infer that the political affiliation affects support for the economic options.