What is indicated when the observed frequencies are substantially different from the expected frequencies?

What is indicated when the observed frequencies are substantially different from the expected frequencies?

• A. The null hypothesis is likely true
• B. The null hypothesis can be rejected
• C. There is no indication of a relationship
• D. The data is perfectly aligned with the hypothesis

Answer: (B)

When observed frequencies differ significantly from expected frequencies, it suggests that the assumptions made by the null hypothesis are not holding true for the data being analyzed. The null hypothesis typically posits that there is no effect or no difference; therefore, a substantial discrepancy between what was expected and what was observed indicates that the situation might be influenced by other factors, leading to the conclusion that the null hypothesis can be rejected. In hypothesis testing, the rejection of the null hypothesis typically means that there is evidence to support an alternative hypothesis, which might assert that a relationship or effect does indeed exist. This conclusion is drawn from statistical analysis tools that measure the degree of difference, often through tests such as the chi-square test. A very high chi-square value, for instance, would point to significant deviations suggesting that the data does not support the hypothesis assumed under the null condition.

When observed frequencies differ significantly from expected frequencies, it suggests that the assumptions made by the null hypothesis are not holding true for the data being analyzed. The null hypothesis typically posits that there is no effect or no difference; therefore, a substantial discrepancy between what was expected and what was observed indicates that the situation might be influenced by other factors, leading to the conclusion that the null hypothesis can be rejected.

In hypothesis testing, the rejection of the null hypothesis typically means that there is evidence to support an alternative hypothesis, which might assert that a relationship or effect does indeed exist. This conclusion is drawn from statistical analysis tools that measure the degree of difference, often through tests such as the chi-square test. A very high chi-square value, for instance, would point to significant deviations suggesting that the data does not support the hypothesis assumed under the null condition.