In the French language, articles change based on the gender and the beginning letter of the noun they accompany. Let's see which article fits with each of the nouns provided:
1. Hôpital: The word "hôpital" begins with a silent 'h' and is masculine. Therefore, the correct article is "à l'" because "hôpital" starts with a vowel sound. Hence, "à l'hôpital" is correct.
2. École: The word "école" is feminine, and since it begins with a vowel sound, the correct article is also "à l'" resulting in "à l'école".
3. Maison: The word "maison" is feminine and begins with a consonant. Therefore, the correct feminine article is "à la", making "à la maison" correct.
4. Cinéma: The word "cinéma" is masculine and starts with a consonant. Therefore, the correct article is "au" (a contraction of "à le"), which gives us "au cinéma".
Since the statement is "J'ai de la fièvre", going to a place typically associated with medical attention is logical. Among the options, "hôpital" is the appropriate choice. Thus, the correct article and noun combination is "à l'hôpital", meaning "I have a fever. I am going to the hospital."