The null hypothesis for a chi-squared goodness-of-fit test is typically that the observed data follow the specified distribution.

Given the options, the correct null hypothesis here is:

d. The age of students enrolled in statistics units in recent semesters at Macquarie University is distributed according to the given table of probabilities.

This aligns with the purpose of a goodness-of-fit test, which evaluates whether observed frequencies differ significantly from expected frequencies based on a specified distribution.

Would you like to explore more details or have any further questions?

Here are five related questions to deepen understanding:

1. What is the alternative hypothesis in this chi-squared goodness-of-fit test?
2. How is the chi-squared statistic calculated in a goodness-of-fit test?
3. What does a very low p-value, such as 5.557e-09, imply in the context of this test?
4. How does the degrees of freedom (df) impact the chi-squared test result?
5. What are some assumptions that need to be met for the chi-squared goodness-of-fit test to be valid?

Tip: When interpreting a chi-squared goodness-of-fit test, always check if the sample size is large enough and that expected frequencies are not too low, as these factors can affect the validity of the results.