In: Statistics and Probability
The researcher believes that recent undergraduates from Connecticut have less debt than the national average. Specify the competing hypotheses to test this belief
Let "mu" be the actual population mean debt of recent undergraduates from Connecticut.
Let "mc" be the actual population mean national debt of Connecticut.
The researcher believes that my is less than mc. The researcher wants to test this belief.
For this testing, the competing hypotheses are:
Null hypothesis is H: mu = mc
Alternative hypothesis is K: mu< mc
The reasearcher will believe his/her claim if and only if, the null hypothesis gets rejected in favour of the alternative hypothesis.
(See null hypothesis always has the sense of nullity. So the equality case is in the null hypothesis. Now the null hypothesis could have been chosen as H: mu >= mc. But as a matter of fact, these two testing becomes equivalent. The researcher's claim is in the alternative hypothesis, because the reasearcher will accept the claim only if the data provedes enough evidence in favour of it.)
Hope the solution helps. Thank you
(If you need further help please ask in the comment section. You may consult any book or internet for further information regarding how hypotheses are set)