The correct spelling of the phrase "study at middle" is debatable, as it is not clear what it is intended to mean. However, if we assume that it is meant to refer to studying at a middle school or in the middle of something, we can use IPA phonetic transcription to explain the spelling. The /st/ sound followed by the long /ʌ/ vowel sound in "study" is spelled with a 'u' because it is pronounced as the unstressed syllable. The short /ɪ/ vowel sound in "middle" is spelled with an 'i' because it is a stressed syllable.