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?

The null hypothesis [tex]H_{0}[/tex] 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 [tex]H_{0}: parameter = value[/tex]

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 [tex]H_{0}: \mu= 185[/tex].

The alternative hypothesis [tex]H_{a}[/tex] 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

[tex]H_{a}: parameter > value\\H_{a}: parameter < value\\H_{a}: parameter \neq value[/tex]

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 [tex]H_{a}: \mu > 185[/tex] as his alternative hypothesis.