Behavioral psychology studies have yielded evidence

It must be E.
A,B eliminated due to sentences not being parallel.
C-"with a failure to ask" does not make sense.
Out of D and E conforming to parallelism, E is the better choice- People "tend to seek out evidence" and "fail to ask".

+1 for E

Studies have indicated 2 things:
1.That People send to seek out evidence that will confirm their hypothesis
2. They fail to ask disconfirming questions.

Meaning clearly reflected in E

The answer is clearly E.

E maintains the perfect parallelism between tend to seek and fail to ask.

Lets have a look on all the other answer choices

A) that indicates that people tend to seek out evidence that will confirm their hypotheses, and failing to ask - makes a false parallelism between a gerund ( failing to ask) and a clause ( that people tend to seek out evidence...)
B) that has indicated people tend to seek out evidence that will confirm their hypotheses, failing to ask-Its unclear what exactly the gerund is trying to modify.
C)indicating that people tend to seek out evidence that will confirm their hypotheses with a failure to ask- changes the meaning completely
D) to indicate that people tended to seek out evidence that will confirm their hypotheses and failed to ask -This option try to make a lousy trap for students by trying to create a parallelism between to indicate and to ask.But its wrong

Here are my two cents (In addition to what techiesam has correctly mentioned)

Option D implies that the studies have yielded evidence for some purpose... And that purpose is indicating people's behavior traits. This clearly distorts the intended meaning.

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Official Explanation

Creating a filter: the original sentence fails to be a grammatical sentence, thanks to the word "and." The phrase after the comma is not part of a list, not a modifier, not the predicate to any sentence, and not an independent clause. Choice (A) is out. We'll look for a choice that solves the basic subject-verb issue.

Applying the filter: choice (B) solves the problem in (A), though it switches the tense of "indicates" to "has indicated." The indicating is a generality, so it should be expressed in the present tense, and choice (B) is eliminated. Choice (C) leaves ambiguous what the "failure to ask" is "with." It seems to say, for example, that people are thinking about hypotheses and the failure together and confirming them both. So (C) is out. Choice (D) has past tenses that are out of place, again, in expressing this finding, which is a generality. We're left with choice (E), which is defect-free.

The correct answer is (E).