Final Answer:
Without specific details about observed frequencies, total sample size, or the expected distribution, it's impossible to calculate the expected frequency for category 4 in the chi-square goodness-of-fit test.The final answer is: C) Not enough information to determine.
Step-by-step explanation:
To calculate the expected frequency in a specific category for the chi-square goodness-of-fit test, several details are required. The chi-square goodness-of-fit test assesses if observed categorical data fits an expected distribution. The expected frequency in a particular category is typically calculated by determining the total sample size, the proportion or probability associated with that category in the expected distribution, and multiplying these values.
However, the question doesn’t provide any specific details regarding the observed frequencies, the total sample size, or the expected distribution's probabilities. Without this essential information, it's impossible to calculate the expected frequency for category 4 accurately. Therefore, the correct answer is C) Not enough information to determine.
In a chi-square goodness-of-fit test, the expected frequency for a category is estimated based on the hypothesized distribution. Without these distribution details or observed frequencies, it's not feasible to ascertain the precise expected frequency for category 4 or any other category.
The test necessitates this fundamental information to compare the observed and expected frequencies, determining whether the observed data aligns significantly or deviates significantly from the expected distribution. Hence, the lack of specific details impedes the calculation of the expected frequency, leading to the answer choice of not having enough information to determine. The final answer is: C) Not enough information to determine.