Final answer:
The statement about the formula for expected frequencies in a chi-square test for independence is true, using the formula stated. Degrees of freedom are calculated as (number of columns - 1)(number of rows - 1). Chi-square tests are right-tailed, and the distribution's shape becomes more symmetrical as degrees of freedom increase.
Step-by-step explanation:
The expected frequencies in a chi-square test for independence are calculated using the formula (row total) × (column total) / total number surveyed. This information is used to compare the observed frequencies with what would be expected if the two variables were independent. For each cell within a contingency table, the expected frequency is calculated by multiplying the sum of the row and the sum of the column the cell falls in and then dividing by the grand total of all observations.
The number of degrees of freedom for the test of independence is determined by the formula df = (number of columns - 1)(number of rows - 1). This is important for identifying the correct chi-square distribution to use when determining the p-value of the test statistic.
It is true that chi-square tests including tests for independence, are right-tailed tests because the distribution is skewed to the right; especially noticeable when the degrees of freedom are low. And, as the degrees of freedom increase, the chi-square distribution becomes more symmetrical.