Answer: To answer this question, we need to know the number of individuals in each combination of Hogwarts elective and house. Without this information, we cannot calculate the expected chi-square test statistic value or the standard deviation.
Assuming we have this information, we can calculate the expected chi-square test statistic value as follows:
Set up a contingency table with the observed frequencies in each cell and the row and column totals.
Calculate the expected frequency for each cell by multiplying the row total by the column total and dividing by the total sample size.
Calculate the chi-square test statistic by summing the squared differences between the observed and expected frequencies for each cell and dividing by the expected frequency for each cell.
The formula for the standard deviation of the chi-square test statistic depends on the degrees of freedom, which is equal to the number of rows minus one multiplied by the number of columns minus one. Once we have calculated the expected chi-square test statistic value and degrees of freedom, we can calculate the standard deviation using the formula:
sqrt(2 * df)
where "df" is the degrees of freedom.
Without the necessary information about the frequencies, we cannot provide a numerical answer to this question.
Explanation: