1.1. The IQ of a student at Calculus High can be modelled as a random variable with the distribution $N(126,50)$ . The headteacher decides to play classical music during lunchtimes and suspects that this has caused a change in the average IQ of the students.

Write suitable null and alternative hypotheses to test the headteacher’s suspicion.

1.2. The headteacher selects 10 students and asks them to complete an IQ test.  Their scores are:

127, 127, 129, 130, 130, 132, 132, 132, 133, 138

Test, at the 5% level of significance, whether there is evidence to support the headteacher’s suspicion.

1.3. It was later discovered that the 10 students used in the sample were all in the same advanced classes.

Comment on the validity of the conclusion of the test based on this information.