the sentence is: Lucy reported that scientists wonder if the medicine will work
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The tree might be correct if one assumes a GB (Government and Binding) theoretical framework from about 1990. The tree is adhering to the standard X-bar schema quite closely, consistently positing three projections for each head (minimal, bar-level, and maximal). But there are some aspects of the tree that are unusual or not clear. The analysis of the C-C'-CP heads is strange. C' should branch downards into C and IP, but it looks instead as though C' is appearing as a second specifier of IP.
Anyone who is learning/drawing these sort of tree structures should be aware of a couple of things about them. The tree appears to be assuming that all branching is binary. This is a widespread assumption in the GB/MP tradition, but there are many frameworks of syntax and grammar that reject the strictly binary branching structures (e.g. HPSG, CxG, DGs). These frameworks assume that branching can also be n-ary at times. Furthermore, a strict adherence to the X-bar schema is no longer consistent with more recent work in the MP (Minimalist Program). The MP assumes bare phrase structure instead of the X-bar schema, which means that the strict adherence to the three levels of a head is no longer necessary.
My overall comment is therefore that one should not take one particular type of tree-analysis for a given sentence too seriously. The analysis will vary significantly based upon the theory of syntax one assumes.