Final answer:
The expected frequencies for a chi-square goodness of fit test are determined by the null hypothesis and can vary between categories. These frequencies are critical for calculating the chi-square statistic to compare expected and observed data.
Step-by-step explanation:
The expected frequencies for each category of a chi-square goodness of fit can differ according to the null hypothesis. This is because the expected frequencies are based on what you would theoretically expect if the null hypothesis were true.
In a chi-square goodness-of-fit test, the calculation of expected frequencies is not arbitrary. Each category's expected frequency is determined based on the specific distribution outlined in the null hypothesis. It's important to note that for the chi-square goodness-of-fit test to be valid, each observed cell or category must have an expected value of at least five. This ensures that the chi-square approximation to the true distribution is sufficiently accurate. If the expected and observed frequencies are significantly different, the resulting chi-square statistic will indicate a poor fit, suggesting that the null hypothesis may be rejected.
The expected frequencies are essential for calculating chi-square statistic, which compares these expected counts to the actual observed counts in the data. The statistic is then used to test the null hypothesis that the observed distribution fits the expected distribution.