A chi-squared goodness-of-fit test is run to answer the research question.
Consider the output of the test below, and answer the questions:


    Chi-squared test for given probabilities

data:  table(var4)
`X-squared = 41.333, df = 3, p-value = 5.557e-09`

What is the null hypothesis? Choose one among the following options:

a. the age of students enrolled in statistics units in recent semesters at Macquarie University is not distributed according to the given table of probabilities

b. the age of students is associated with student enrolment type (domestic or international)

c. the age of students and student enrolment type (domestic or international) are independent

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

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.

A chi-squared goodness-of-fit test is run to answer the research question. Consider the output of the test below, and answer the questions:

Chi-squared test for given probabilities

table(var4)
`X-squared = 41.333, df = 3, p-value = 5.557e-09`

What is the null hypothesis? Choose one among the following options:

a. the age of students enrolled in statistics units in recent semesters at Macquarie University is not distributed according to the given table of probabilities

b. the age of students is associated with student enrolment type (domestic or international)

c. the age of students and student enrolment type (domestic or international) are independent

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

Explore the chi-squared goodness-of-fit test, focusing on hypothesis selection based on statistical output. This test evaluates if observed data follow a specified distribution, with example analysis for student age distribution in university statistics courses. Ideal for undergraduate students studying hypothesis testing.

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