Question

A recent article in a university newspaper claimed that the proportion of students who commute more than miles to school is no more than . Suppose that we suspect otherwise and carry out a hypothesis test. State the null hypothesis and the alternative hypothesis that we would use for this test.

Answer 1

The null hypothesis is
`H_0: p \leq x`, in which x is the proportion tested.

The alternative hypothesis is
`H_1: p > x`

Explanation:

A recent article in a university newspaper claimed that the proportion of students who commute more than miles to school is no more than x.

This means that at the null hypothesis, we test if the proportion is of at most x, that is:

`H_0: p \leq x`

Suppose that we suspect otherwise and carry out a hypothesis test.

The opposite of at most x is more than x, so the alternative hypothesis is:

`H_1: p > x`