You obtain a sample chi-square value of χ2=−5.49. On the basis of this value, you know thata. there is a negative association between your two variables.b. the observed frequencies are higher than the expected frequencies across at least half of your cells.c. you have made a calculation error; chi-square values cannot be negative.d. the observed frequencies are lower than the expected frequencies across all cells.

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Painiaerocaaph · Accepted Answer

Given: The observed/calculated value of χ2=−5.49.The value of the chi-square test statistic is calculated as:χ2=∑(O−E)2EExplanation to correct option:c. The observed value is calculated as the sum of the square of the difference between the observed and expected frequencies divided by the expected frequency. Therefore, the square will make the sum positive, and hence, the observed value can not be negative and it is clear that some errors in the calculations have been made and the value cannot be negative.Thus, option c. is correct.Explanation to incorrect options:a. The calculated value of the Chi-square test helps in finding the relationship and independence between the two variables. As the value of the test statistic is the sum of the square of the difference between observed and expected frequency. Therefore, the observed value can not be negative, and hence, there will not be a negative association between the variables.Thus, option a. is incorrect.b. The given observed value of the Chi-square test is -5.49. Therefore, It cannot be said that the observed frequencies are higher than the expected frequencies across at least half of your cells because the value will be calculated by squaring the difference between the frequencies. Hence, the higher value of observed frequencies or expected frequencies does not affect the sign of the calculated test statistics.Thus, option b. is incorrect.

Misurina6am · Accepted Answer

What about d.?d. If the observed frequencies are lower than the expected frequencies across all cells. It will not make a difference in the sign of the chi-square test statistics. Hence, option d. is incorrect.

You obtain a sample chi-square value of \chi^2= -5.49. On the basis of this value, you know th

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