Question

I need help with this problem.

1. Chi-Square Test

1. A researcher is interested in determining whether an association exists between successful campaign fund raising and political success in elections. The following cross- tabulation displays the data she collected about the amount raised (characterized as either High/Low) and overall political success (coded as Successful/Not Successful). Calculate the chi-square and interpret your results. Assume an alpha = .05.

	Fund Raising
Political Success	Low	High	Totals
Not Successful	24	6	30
Successful	8	22	30
Totals	32	28	60

	fo	fe	fo -fe	(fo -fe)2	(fo -fe)2 / fe
No Success & Low Funds	24
Success & Low Funds	8
No Success & High Funds	6
Success & High Funds	22

1. State the null and research hypotheses.

2. State the level of significance.

3. State the formula for the test-statistic you will use (and df, if appropriate).

4. Determine your critical test-statistic score.

5. Calculate your research test-statistic score.

6. Interpret your finding in the context of the problem.

Answer 1

The following cross-tabulation have been provided. The row and column total have been calculated and they are shown below:

	Low	High	Total
Not Successful	24	6	30
Successful	8	22	30
Total	32	28	60

The expected values are computed in terms of row and column totals. In fact, the formula is , where R_i corresponds to the total sum of elements in row i, C_j corresponds to the total sum of elements in column j, and T is the grand total. The table below shows the calculations to obtain the table with expected values:

Expected Values	Low	High	Total
Not Successful			30
Successful			30
Total	32	28	60

Based on the observed and expected values, the squared distances can be computed according to the following formula:. The table with squared distances is shown below:

Squared Distances	Low	High
Not Successful
Successful

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H_0 ​: The two variables are independent

H_a ​: The two variables are dependent

This corresponds to a Chi-Square test of independence.

Rejection Region

Based on the information provided, the significance level is α=0.05 , the number of degrees of freedom is df = (2 - 1) \times (2 - 1) = 1.

Test Statistics

The Chi-Squared statistic is computed as follows:

Since it is observed that = 17.143 > = 3.841, it is then concluded that the null hypothesis is rejected.

Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the two variables are dependent, at the 0.05 significance level.

The corresponding p-value for the test is

	fo	fe	fo -fe	(fo -fe)2	(fo -fe)2 / fe
No Success & Low Funds	24	16	8	64	4
Success & Low Funds	8	16	-8	64	4
No Success & High Funds	6	14	-8	64	4.571
Success & High Funds	22	14	8	64	4.571

State the null and research hypotheses

H_0 ​: The two variables are independent

H_a ​: The two variables are dependent

State the level of significance.

the significance level is α=0.05

State the formula for the test-statistic you will use (and df, if appropriate).

Determine your critical test-statistic score.

= 3.841

Calculate your research test-statistic score.

= 17.143

Interpret your findings in the context of the problem.

the two variables are dependent, at the 0.05 significance level.