Nota sobre NO CREER

The negative constructions of creer and pensar (no creer que and no pensar que) may be followed by the indicative as well as the subjunctive.  The choice of the indicative by the speaker suggests he/she thinks the event in the dependent clause is definitely NOT going to happen or is definitely NOT the case,  while the use of the subjunctive suggests that the speaker is less certain about the event.

No creo que Lola y Paco vayan al cine.   (I don't think Lola and Paco are going to the movies.  Speaker isn't sure whether Lola and Paco are going to the movies or not--it's possible they are going.)

No creo que Lola y Paco van al cine.  (I don't think Lola and Paco are going to the movies.  Speaker believes Lola and Paco are NOT going to the movies.  The speaker is 99.9% certain they are NOT going to the movies.)

(The above is adapted from Repaso: A Complete Review Workbook for Grammar, Communication, and Culture (Lincolnwood, IL: National Textbook, 1998), p. 177.

Zenia Sacks da Silva  (A Concept Approach to Spanish) puts it another way:  No creer "will produce a subjunctive if the student wishes to cast doubt on the subordinate clause action, and the indicative if he makes no implication of doubt."

No creo que lo cojan.  I don't think (I doubt) that they will catch him.
No creo que lo cogerán. I don't believe that they will catch him.  (I fully believe that they will not catch him.)

Nota sobre Práctica 14, p. 109 (Holton et al., Spanish Grammar in Review)

Práctica 14 is set up to give you practice in sequencing of tenses.  It is understood for this exercise that all sentences will contain two clauses: an independent clause (main clause) and a dependent clause (a subordinate noun clause) and that the dependent (subordinate) clause will have a subjunctive.  The basic task is to determine what tenses should be used in each clause and then to translate the sentences.

Romeo y Julieta querían casarse.  (information to be used in the subordinate clause of the translated sentence):

I didn't believe they wanted to get married.
No creía que quisieran casarse.

(If you say "No creía que querían casarse," you are basically saying that you were practically certain  that they did NOT want to get married.)

By its nature "no creer" connotes strong doubt, denial, and non-belief or disbelief.  These concepts generally trigger subjunctive.  The recommended  modus operandi is to use subjunctive in a que- clause after no creer and indicative in a que-clause after creer.

Creo que Jorge y Ana quieren casarse.
No creo que Jorge y Ana quieran casarse antes de graduarse de la universidad.