Final Answer:
The goodness-of-fit test between the observed class frequencies and the expected frequencies of a normal distribution with μ = 64 and σ = 21, using a significance level of 0.05, does not support a good fit.
Explanation:
The chi-square goodness-of-fit test was conducted to assess the match between observed and expected frequencies based on the given elementary statistics course grades. The calculated chi-square statistic, compared against the critical value from the chi-square distribution with appropriate degrees of freedom (n - 1), leads to the conclusion that the observed frequencies significantly deviate from those expected in a normal distribution with μ = 64 and σ = 21 at a 0.05 significance level.
This suggests that the grades do not align well with a normal distribution with the specified mean and standard deviation. The chi-square statistic derived from the data falls beyond the critical value, indicating a substantial discrepancy between the observed and expected frequencies. Consequently, the hypothesis of a good fit between the observed class frequencies and the expected frequencies of a normal distribution is rejected.
The goodness-of-fit test allows us to scrutinize the conformity of observed data to an expected theoretical distribution. In this case, the elementary statistics course grades diverge significantly from what would be anticipated under a normal distribution with a mean of 64 and a standard deviation of 21. The rejection of the hypothesis at the 0.05 significance level implies that the observed grades distribution differs significantly from a normal distribution with the specified parameters.