What would be a nondirectional hypothesis for this statement. Older drivers are safer than younger ones. I have this not sure if it is correct. There will be a difference between older and younger drivers.
HO:p=R
Directional:
HA≥R
or
HA≤R
Nondirectional:
HA≠R
Directional hypotheses have alternate hypotheses that point in some direction as to having a value less than or greater than the quantity denoted by the null hypothesis. Nondirectional hypotheses simply state that the alternate hypothesized value is different than the null hypothesized value.
In your example...
HO:p=∂older−∂younger=0
HA:p≤0
where "∂" represents the total accident occurrence rate in set age groups (older = 31+; younger = 16-30) in the past year.
This is unidirectional because it hypothesizes that the trend of accident occurrences/driving safety rates in variant age groups tends toward one direction.
To make the hypothesis nondirectional, simply reword the hypothesis such that it doesn't indicate the general trend of accident occurrences/driving safety rates tending towards one direction. EXAMPLE: An insurance company asks you to determine whether a difference exists in the accident rates between younger and older drivers.
A nondirectional hypothesis for the statement "Older drivers are safer than younger ones" would be:
There is a difference in safety between older and younger drivers.
To explain how to form this hypothesis, you start by identifying the two groups you want to compare, in this case, older drivers and younger drivers. Then, you need to express the expectation or assumption that there is a difference between these two groups regarding the topic of interest, which is safety in this case.
Since it isn't specified whether older drivers are expected to be safer or less safe than younger drivers, a nondirectional hypothesis is appropriate. It simply states that there is a difference between the two groups without specifying the direction of that difference.