In chi square goodness of fit test, if the expected frequencies, and the observed frequencies were quite different, we could conclude that:
A) null hypothesis is false, and we would reject
B) chi square distribution is invalid, and use t distribution instead
C) alternate hypothesis is false, and reject
A, assuming it exceeds you level of significance.
To determine the correct answer, we need to understand the chi-square goodness of fit test. The chi-square goodness of fit test is a statistical test used to determine whether observed categorical data significantly differs from expected values. This test involves comparing the observed frequencies (data actually collected) with the expected frequencies (data expected if the null hypothesis is true) to evaluate if there is a meaningful difference.
Based on the given information that the expected and observed frequencies are quite different, we can conclude that the null hypothesis is false and we should reject it. This means that choice A) "null hypothesis is false, and we would reject" is the correct answer.
To perform a chi-square goodness of fit test, you would need to follow these steps:
1. Formulate the null and alternative hypotheses. The null hypothesis assumes that there is no significant difference between the observed and expected frequencies, while the alternative hypothesis suggests that there is a significant difference.
2. Select a significance level (alpha) to determine the threshold for accepting or rejecting the null hypothesis. Commonly used values for alpha are 0.05 or 0.01.
3. Determine the expected frequencies for each category under the null hypothesis. These can be calculated based on theoretical probabilities or by using historical data as a reference.
4. Collect data and calculate the observed frequencies for each category.
5. Calculate the chi-square test statistic using the formula: X^2 = Σ((O - E)^2 / E), where O is the observed frequency and E is the expected frequency for each category. Sum up the contributions for all categories.
6. Determine the degrees of freedom (df). In a goodness of fit test, df equals the number of categories minus 1.
7. Use a chi-square distribution table or a statistical software to determine the critical value of chi-square for the given significance level and degrees of freedom.
8. Compare the calculated chi-square test statistic to the critical value. If the calculated value is greater than the critical value, it suggests a significant difference between the observed and expected frequencies, leading to the rejection of the null hypothesis. However, if the calculated value is less than or equal to the critical value, it indicates that the observed frequencies do not significantly differ from the expected frequencies, and the null hypothesis cannot be rejected.
Therefore, in this case, since the observed and expected frequencies are quite different, it can be concluded that the null hypothesis is false and should be rejected.