Answer to Question #154651 in Statistics and Probability for chi 4

Question

One of the issues that came up in a recent national

election (and is likely to arise in many future elections)

is how to deal with a sluggish economy.

Specifically, should governments cut spending, raise

taxes, inflate the economy (by printing more money)

or do none of the above and let the deficit rise? And

as with most other issues, politicians need to know

which parts of the electorate support these options.

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?

Economic

Options

Political Affiliation

Democrat Republican Independent

Cut spending 101 282 61

Raise taxes 38 67 25

Inflate the

economy 131 88 31

Let deficit

increase 61 90 25

Answer 1

The given information:

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 for testing null hypothesis is

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

k = the number of cells in the cross-classification table

e_i = the expected frequencies

f_i = observed frequencies

Using MINITAB, we conduct the above test of null hypothesis against the alternative hypothesis in 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 χ² = 70.675

The P-value is 0.000

Here we observe that, the P-value is less than the level of the significance 0.05, 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.