Question

It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. Identify the correct null and alternative hypotheses to test the politician’s claim. Multiple Choice H0: p = 0.50 and HA: p ≠ 0.50 H0: p ≤ 0.50 and HA: p > 0.50 H0: p ≥ 0.50 and HA: p > 0.50 H0: p ≥ 0.50 and HA: p < 0.50

Answer 1

`H_0` : p ≤ 0.50 and
`H_A` : p > 0.50

Explanation:

We are given that it is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock.

A politician claims that the proportion of babies born out of wedlock is increasing.

Let p = population proportion of babies who born out of wedlock

So, Null Hypothesis,
`H_0` : p
`\leq` 0.50

Alternate Hypothesis,
`H_A` : p > 0.50

Here, the null hypothesis states that the proportion of babies who born out of wedlock is no more than 0.50 or 50%.

And alternate hypothesis states that the proportion of babies who born out of wedlock is increasing.

After testing this hypothesis we will conclude that whether null hypothesis be accepted or rejected.

Therefore, the correct null and alternative hypotheses to test the politician’s claim would be
`H_0` : p ≤ 0.50 and
`H_A` : p > 0.50.