Chi-squared hypothesis tests

The Department of Education is doing an analysis on the higher education of learners

who have passed Grade 12. A study conducted last year found that 40% of learners

had gone to a university, 25% had enrolled for a diploma, 20% had enrolled for a

certificate in higher education, and 15% had started working. As a marketing intern at

the Department of Education, you conducted a recent survey among 500 randomly

selected learners and found that 205 learners had gone to university, 105 had

enrolled for a diploma, 80 had enrolled for a certificate in higher education and the

rest had started working. Use a 5% level of significance for this test. (Use a critical

value of 7,815.)

1. Determine the null hypothesis needed to run a goodness-of-fit test.

2. Calculate the expected frequency for the possibility of going to university.

3. Calculate the expected frequency for the possibility of enrolling for a

diploma.

4. Calculate the expected frequency for the possibility of enrolling for a

certificate.

5. Calculate the expected frequency for the possibility of starting to work.

6. Is the following statement true or false? The chi-squared statistic is given as

23,66, therefore rejecting the null hypothesis, as 23,66 falls outside the range

of acceptance and 23,66 is higher than 7,815.

7. What level of confidence would you have in your findings?