Question

For the following hypothesis​ test, determine the null and alternative hypotheses.​ Also, classify the hypothesis test as two​ tailed, left​ tailed, or right tailed. The mean local monthly bill for cell phone users in this country was ​$47.79 in 2001. A hypothesis test is to be performed to determine whether last​ year's mean local monthly bill for cell phone users has decreased from the 2001 mean of ​$47.79.

Answer 1

The null and alternative hypothesis are:

`H_0: \mu=47.79\\\\H_a:\mu< 47.79`

This is a left tailed test.

Explanation:

A hypothesis test is to be performed to determine whether last​ year's mean local monthly bill for cell phone users has decreased from the 2001 mean of ​$47.79.

Then, the claim that will be expressed in the alternative hypothesis is that the monthly bill is lower than $47.79.

The null hypothesis will state that the monthly bill does not differ significantly from $47.79.

Then, the null and alternative hypothesis are:

`H_0: \mu=47.79\\\\H_a:\mu< 47.79`

As we only want to test if its lower, we are interested only in the left tail of the distribution. We want to know if the test statistic is below the critical value to conclude if we have evidence for our claim. This is then a left tailed test.