Question

A SCUBA instructor wants to record the collective depths each of his students dives during their checkout. He is interested in how the depths vary, even though everyone should have been at the same depth. He believes the standard deviation is three feet. His assistant thinks the standard deviation is less than three feet. If the instructor were to conduct a test, what would the null and alternative hypotheses be?

Short answer

The null hypothesis is$H_0:{\sigma }^2=3^2$

The alternative hypothesis is as follows:$H_a:{\sigma }^2<3^2.$

Step-by-step solution

Given information

Given in the question that, a SCUBA instructor wants to record the collective depths each of his students dives during their checkout. He is interested in how the depths vary, even though everyone should have been at the same depth. He believes the standard deviation is three feet. His assistant thinks the standard deviation is less than three feet. We need to find the null and alternative hypotheses if the instructor were to conduct a test.

Explanation

During their checkout, a SCUBA teacher wants to record the total depths of each of his students' dives. He's curious in how the depths differ, despite the fact that everyone should have been at the same depth. The standard deviation, he says, is three feet. The standard variation, according to his aide, is less than three feet.

Calculation:

The null hypothesis is$H_0:{\sigma }^2=3^2$

The alternative hypothesis$H_a:{\sigma }^2<3^2.$