Final answer:
To determine the chi-square test-statistic for a contingency table, calculate the expected frequencies for each cell, then sum the square of the difference between observed and expected frequencies divided by the expected frequency. The formula for degrees of freedom is the number of rows minus one times the number of columns minus one. The chi-square test is right-tailed.
Step-by-step explanation:
To calculate the chi-square test-statistic for given data, we must first find the expected frequencies for each cell in the contingency table. The chi-square test-statistic (χ2) is computed using the formula:
χ2 = ∑ [(O - E)2 / E]
where O is the observed frequency and E is the expected frequency for a cell. The expected frequency is calculated as:
E = (row total × column total) / total number surveyed
After calculating the expected frequencies, we compute the chi-square test-statistic by summing the square of the difference between observed and expected frequencies divided by the expected frequency for each cell.
The formula for the degrees of freedom (df) is given by:
df = (number of rows - 1)(number of columns - 1)
The chi-square test of independence always has a right-tailed distribution, as the test statistic becomes larger when there is a significant difference between observed and expected values.