Can confirmatory factor analysis be used to test a hypothesis about a one-factor solution I want to test the hypothesis that observed variables can be explained by one latent variable (factor), does a confirmatory factor analysis allow me to test such a hypothesis? 
Example:


*

*Data: 200 responses on 23 questions (measured on a 5-point Likert scale)

*Method: confirmatory factor analysis with one factor loading on all the questions

*Hypothesis: One factor is sufficient to explain the variation in the observed variables


Can I say it tests my hypothesis that a one factor is sufficient to explain the observed data? What is the null hypothesis in confirmatory factor analysis? 
 A: Testing the model structure is exactly what confirmatory factor analysis does. The null hypothesis is "The hypothesized structure fits the data well" vs. a non-committal alternative "The hypothesized structure does not fit the data well enough", which includes alternatives like "more factors are needed" or "some unique errors for items are correlated", but you need to construct these specific alternatives to look into these specific tests.
Personally, I think EFA is only applicable when you know NOTHING about your object of the study. If you constructed your instrument with an idea in mind of measuring some psychological construct, you implicitly have that single factor model built into it. If you know that you have several subscales, then you should fit a CFA that has that many factors, or may be a hierarchical CFA with one higher level factor. But running an EFA to say "Gee, turns out we have three factors in this scale... or wait, let me try a different rotation" -- that does not seem very scientific to me.
