We assume that 80% of the children who perform well at school get a university degree later in their life. To verify this assumption, we conduct a small poll with 100 participants. Of those, 75 did well at school and then obtained a university degree.

In what follows, we would like to interpret the assumption above as a test problem, and use the likelihood ratio test statistic () to test for the null hypothesis H0.

1. What statistical model would you use in the context of this study?
2. Formulate an appropriate test problem, i.e., provide the hypotheses H0 and H1, to check for the assumption above.
3. Derive the likelihood ratio test statistic (0). Note: No derivation of the corresponding likelihood function is required.
4. Using the data above, determine the observed value (0) of the test statistic in (c).
5. Using your result in (d), calculate the corresponding p-value to test H0 in the test problem formulated in (b).