Question

Previously, an organization reported that teenagers spent an average of 4.1 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 5.25 hours with a sample standard deviation of 2.0. What are the null and alternate hypotheses?

Answer 1

Answer:

$H_0:\mu\leq4.1\\H_1: \mu>4.1$

Step-by-step explanation:

In this case,  the claim the organization is making is that the average of hours per week teenagers are spending on the phone is higher.

If we use hypoyhesis testing to prove that, we have to know we have two possible results:

1. The null hypothesis is rejected. In this case the sample gives enough evidence to prove that the null hypothesis is not true. That makes the alternative hypothesis became true.
2. The null hypothesis is failed to be rejected. In this case, there is no enough evidence to prove wrong the null hypothesis, so we can't claim that the alternative hypothesis is true.

Then, we have to write a null hypothesis that, if it is rejected, prove that the claim or the organization is true.

In this case the null hypothesis would be that the mean is (still) 4.1 hours or less, and the alternative hypothesis (what the organization claims) is that the mean is higher than 4.1:

$H_0:\mu\leq4.1\\H_1: \mu>4.1$