Question

An investigator wants to assess whether the mean m = the weight of passengers flying on small planes exceeds the FAA guideline of the average total weight of 185 pounds (passenger weight including shoes, clothes, and carry-on). Suppose that a random sample of 51 passengers showed an average total weight of 200 pounds with a sample standard deviation of 59.5 pounds. Assume that passenger total weights are normally distributed. What are the appropriate null and alternative hypotheses?

Answer 1

`H_(0): \mu= 185` and
`H_(a): \mu > 185`

Explanation:

The null hypothesis
`H_(0)` states that a population parameter (such as the mean, the standard deviation, and so on) is equal to a hypothesized value. We can write the null hypothesis in the form
`H_(0): parameter = value`

In this context, the investigator's null hypothesis should be that the average total weight is no different than the reported value by the FAA. We can write it in this form
`H_(0): \mu= 185`.

The alternative hypothesis
`H_(a)` states that a population parameter is smaller, greater, or different than the hypothesized value in the null hypothesis. We can write the alternative hypothesis in one of three forms

`H_(a): parameter > value\\H_(a): parameter < value\\H_(a): parameter \\eq value`

The investigator wants to know if the average weight of passengers flying on small planes exceeds the FAA guideline of the average total weight of 185 pounds. He should use
`H_(a): \mu > 185` as his alternative hypothesis.